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Recent questions and answers in Application of Derivatives
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Application of Derivatives
The function $ f(x)=2 log (x-2) - x^2+4x+1 $increases in the interval.\[(a)\;(1,2)\qquad(b)\;(2,3)\qquad(c)\;(5/2,3)\qquad(d)\;(2,4)\]
cbse
class12
additionalproblem
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ch6
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p16
math
answered
Mar 7
by
ranjani.hogwarts
1
answer
If the line ax+by+c = 0 is normal to the curve xy = 1 then \[(a)\;a>0,b>0 \qquad (b)\;a<0,b<0 \qquad(c)\;a<0,b>0\qquad(d)\;a<0,b<0.\]
cbse
class12
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kvquestionbank2012
ch6
q13
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math
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Jul 5, 2017
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toshit.jain
1
answer
find intervals in which function given by f(x) = sin 3x where x belongs [0, pi/2] is 1 increasing 2 decreasing
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May 13, 2017
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nikunjjain285
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The two equal sides of an isosceles triangle with fixed base b are decreasing at the rate of 3 cm per second. How fast is the area decreasing when the two equal sides are equal to the base ?
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ch6
sec-e
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Dec 8, 2016
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priyanka.c
1
answer
The radius of a circle is increasing uniformly at the rate of 3 cm/s. How fast is the volume of the cube increasing when the edge is 10cm long ?
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ch6
sec-e
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Dec 7, 2016
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The total revenue in Rupees received from the sales of $x$ units of a product is given by $Rx = 3x^2 + 36x +5$ . Find the marginal revenue , when $x=15$, where by marginal.
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class12
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Dec 6, 2016
by
priyanka.c
1
answer
application of derivatives
asked
Mar 4, 2016
by
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0
answers
An open box with square base is to be made of a given quantity of card board of area $ 36 sq.metre.$ Find the maximum volume of the box.
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class12
ch6
q29
p137
exemplar
medium
sec-c
math
answered
Feb 4, 2014
by
rvidyagovindarajan_1
1
answer
A man, 2m tall, walks at the rate of $1\frac{2}{3}m/s$ towards a street light which is $5\frac{1}{3}m$ above the ground.At what rate is the tip of his shadow moving?At what rate is the length of the shadow changing when he is $3\frac{1}{3}m$ from the base of the light?
cbse
class12
ch6
q8
p135
short-answer
exemplar
difficult
sec-b
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answered
Jan 20, 2014
by
balaji.thirumalai
1
answer
question no. 25 of exercise 6.5
class12
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exercise
6
5
q
25
answered
Jan 11, 2014
by
balaji.thirumalai
1
answer
SHOW THAT THE SEMI VERTICAL ANGLE OF THE CONE OF THE MAXIMUM VOLUME AND OF GIVEN SLANT HEIGHT IS
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Jan 9, 2014
by
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0
answers
question no. 25 of exercise 6.5
class12
math
exercise
6
5
q
25
asked
Jan 9, 2014
by
guptaaakanksha2_1
0
answers
question no. 25 of exercise 6.5
class12
math
exercise
6
5
q
25
asked
Jan 9, 2014
by
guptaaakanksha2_1
0
answers
question no. 25 of exercise 6.5
asked
Jan 9, 2014
by
guptaaakanksha2_1
0
answers
Show that the height of the cylinder of maximum volume that can be inscribed in a sphere of radius R is \(\large\frac{2R}{\sqrt 3}\) . Also find the maximum volume.
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class12
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ch6
misc
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p243
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Jan 6, 2014
by
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2
answers
Find the maximum area of an isosceles triangle inscribed in the ellipse $\large\frac{x^2}{a^2} + \frac{y^2}{b^2} $$= 1 $ with its vertex at one end of the major axis.
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class12
bookproblem
ch6
misc
q8
p242
sec-b
medium
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Jan 6, 2014
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2
answers
Find the equation of the tangent and normal to the curve $ \;y=\large\frac{1+\sin x}{\cos x}$ at $\;x=\large\frac{\pi}{4}$
cbse
class12
additionalproblem
ch6
sec-b
easy
math
answered
Dec 23, 2013
by
balaji.thirumalai
1
answer
The cost of construction for an open tank is Rs. 200 per sq. unit for the base, and the cost for doing the walls is Rs. 150 per sq. unit. An open tank is to be constructed with rectangular base of height 2 units and volume of 8 cubic units.What is the cost of the least expensive open tank given these constraints?
cbse
class12
additionalproblem
ch6
sec-c
easy
math
answered
Dec 23, 2013
by
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1
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If the radius of a sphere is measured as $70$ cm with an error of $0.03$cm, then find the approximate error in calculating its surface area
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class12
easy
sec-a
ch6
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additionalproblem
math
answered
Dec 22, 2013
by
balaji.thirumalai
1
answer
The length x of a rectangle is decreasing at the rate of 5 cm/minute and the width y is increasing at the rate of 4 cm/minute. When x = 8 cm and y = 6 cm, find the rate of change of (a) the perimeter, (b) the area of the rectangle.
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class12
modelpaper
2012
sec-b
q15
difficult
ch6
math
answered
Nov 15, 2013
by
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1
answer
Find the maximum value of \(2x^3 – 24x + 107\) in the interval \([1, 3]\).
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class12
bookproblem
ch6
sec5
q10
q10-1
p232
sec-b
easy
math
answered
Aug 19, 2013
by
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1
answer
Find the intervals in which the function $f$ given by $f (x) = 2x^2 - 3x$ is $(a) \;strictly\; increasing$
cbse
class12
bookproblem
ch6
sec2
q4
q4-b
p205
sec-b
easy
math
answered
Aug 16, 2013
by
sreemathi.v
1
answer
The interval on which the function $f(x)=2x^3+9x^2+12x-1$ is decreasing is :
cbse
class12
ch6
q46
p140
objective
exemplar
easy
sec-a
math
answered
Aug 13, 2013
by
thanvigandhi_1
1
answer
Two curves $x^3-3xy^2+2=0$ and $3x^2-y^3-2=0$ intersect at an angle of
cbse
class12
ch6
q45
p140
objective
exemplar
sec-a
difficult
math
answered
Aug 13, 2013
by
thanvigandhi_1
1
answer
The least value of the function $f(x)=ax+\frac{b}{x}(a>0,b>0,x>0)$ is ___________.
cbse
class12
ch6
q64
p142
fitb
exemplar
sec-a
medium
math
answered
Aug 13, 2013
by
thanvigandhi_1
1
answer
The function $f(x)=\Large\frac{2x^2-1}{x^4}$,x>0,decreases in the interval__________.
cbse
class12
ch6
q63
p142
fitb
exemplar
medium
sec-a
math
answered
Aug 13, 2013
by
thanvigandhi_1
1
answer
The value of a for which the function $f(x)=sin x-ax+b$ increases on R are__________.
cbse
class12
ch6
q62
p142
fitb
exemplar
sec-a
medium
math
answered
Aug 13, 2013
by
thanvigandhi_1
1
answer
The equation of normal to the curve y=tan x at (0,0) is___________.
cbse
class12
ch6
q61
p142
fitb
exemplar
sec-a
easy
math
answered
Aug 13, 2013
by
thanvigandhi_1
1
answer
The curves $y=4x^2+2x-8$ and $y=x^3-x+13$ touch each other at the point_________.
cbse
class12
ch6
q60
p142
fitb
exemplar
sec-a
medium
math
answered
Aug 13, 2013
by
thanvigandhi_1
1
answer
The maximum value of $\Large\frac{1}{x}$ is:
cbse
class12
ch6
q59
p141
objective
exemplar
sec-a
difficult
math
answered
Aug 13, 2013
by
thanvigandhi_1
1
answer
Choose the correct answer in the points on the curve \(9y^2 = x^3\), where the normal to the curve makes equal intercepts with the axes are
cbse
class12
bookproblem
ch6
misc
q24
p244
sec-b
easy
math
answered
Aug 13, 2013
by
sreemathi.v
1
answer
Choose the correct answer in the normal to the curve \(x^2 = 4y\) passing \((1,2)\) is
cbse
class12
bookproblem
ch6
misc
q23
p244
sec-c
medium
math
answered
Aug 13, 2013
by
sreemathi.v
1
answer
Choose the correct answer in the normal at the point \((1,1)\) on the curve \(2y + x^2 = 3\) is
cbse
class12
bookproblem
ch6
misc
q22
p244
sec-a
medium
math
answered
Aug 13, 2013
by
sreemathi.v
1
answer
Choose the correct answer in the line \(y = mx + 1\) is a tangent to the curve \(y^2 = 4x\) if the value of \(m\) is
cbse
class12
bookproblem
ch6
misc
q21
p244
sec-b
medium
math
answered
Aug 13, 2013
by
sreemathi.v
1
answer
Choose the correct answer in the slope of the tangent to the curve \(x = t^2 + 3t – 8, y = 2t^2 – 2t – 5\) at the point \((2,– 1)\) is
cbse
class12
bookproblem
ch6
misc
q20
p243
sec-b
medium
math
answered
Aug 13, 2013
by
sreemathi.v
1
answer
Choose the correct answer in a cylindrical tank of radius 10 m is being filled with wheat at the rate of 314 cubic metre per hour. Then the depth of the wheat is increasing at the rate of
cbse
class12
bookproblem
ch6
misc
q19
p243
sec-a
medium
math
answered
Aug 13, 2013
by
sreemathi.v
1
answer
Show that height of the cylinder of greatest volume which can be inscribed in a right circular cone of height \(h\) and semi vertical angle $\alpha$ is one-third that of the cone and the greatest volume of cylinder is $\large \frac{4}{27}$$\pi h^3 \: tan^2 \: \alpha $
cbse
class12
bookproblem
ch6
misc
q18
p243
sec-c
medium
math
answered
Aug 13, 2013
by
sreemathi.v
1
answer
$f(x)=x^x$ has a stationary point at
cbse
class12
ch6
q58
p141
objective
exemplar
sec-a
difficult
math
answered
Aug 12, 2013
by
thanvigandhi_1
1
answer
Maximum slope of the curve $y=x^3+3x^2+9x-27$ is
cbse
class12
ch6
q57
p141
objective
exemplar
sec-a
medium
math
answered
Aug 12, 2013
by
thanvigandhi_1
1
answer
At $x=\Large\frac{5}{6}$$,f(x)=2\sin 3x+3\cos 3x$ is:
cbse
class12
ch6
q56
p141
objective
exemplar
sec-a
medium
math
answered
Aug 12, 2013
by
thanvigandhi_1
1
answer
Let \(f\) be a function defined on \([a, b]\) such that \(f' (x) > 0\), for all \(x \: \in (a, b)\). Then prove that \(f\) is an increasing function on \((a, b).\)
cbse
class12
bookproblem
ch6
misc
q16
p243
sec-b
medium
math
answered
Aug 12, 2013
by
sreemathi.v
1
answer
The maximum value of sin x,cos x is
cbse
class12
ch6
q55
p141
objective
exemplar
sec-a
medium
math
answered
Aug 12, 2013
by
thanvigandhi_1
1
answer
The function $f(x)=2x^3-3x^2-12x+4$,has
cbse
class12
ch6
q54
p141
objective
exemplar
medium
sec-a
math
answered
Aug 12, 2013
by
thanvigandhi_1
1
answer
Show that the altitude of the right circular cone of maximum volume that can be inscribed in a sphere of radius \(r\) is \( \large\frac{4r}{3}\)
cbse
class12
bookproblem
ch6
misc
q15
p243
sec-b
medium
math
answered
Aug 12, 2013
by
sreemathi.v
1
answer
Find the absolute maximum and minimum values of the function $(f)$ given by $ f (x) = cos^2 x + sin\: x, x\: \in [0, \pi]$
cbse
class12
bookproblem
ch6
misc
q14
p243
sec-b
easy
math
answered
Aug 12, 2013
by
sreemathi.v
1
answer
Find the points at which the function \(f\) given by \(f (x) = (x – 2)^4 (x + 1)^3\) has a (i) local maxima, (ii) local minima and the (iii) point of inflexion.
cbse
class12
bookproblem
ch6
misc
q13
p243
sec-b
easy
math
answered
Aug 12, 2013
by
sreemathi.v
1
answer
A point on the hypotenuse of a triangle is at distance \(a\) and \(b\) from the sides of the triangle.Show that the maximum length of the hypotenuse is $ (a^{\large\frac{2}{3}} + $$b^{\large\frac{2}{3}})^{\Large\frac{3}{2}}$
cbse
class12
bookproblem
ch6
misc
q12
p243
sec-c
difficult
math
answered
Aug 12, 2013
by
sreemathi.v
1
answer
A window is in the form of a rectangle surmounted by a semicircular opening. The total perimeter of the window is 10 m. Find the dimensions of the window to admit maximum light through the whole opening.
cbse
class12
bookproblem
ch6
misc
q11
p243
sec-c
medium
math
answered
Aug 12, 2013
by
sreemathi.v
1
answer
The sum of the perimeter of a circle and square is \(k\), where \(k\) is some constant. Prove that the sum of their areas is least when the side of square is double the radius of the circle.
cbse
class12
bookproblem
ch6
misc
q10
242
sec-b
easy
modelpaper-2014
modelpaper-2012
q28
math
answered
Aug 12, 2013
by
sreemathi.v
1
answer
The smallest value of the polynomial $x^3-18x^2+96x$ in [0,9] is
cbse
class12
ch6
q53
p141
objective
exemplar
difficult
sec-c
math
answered
Aug 11, 2013
by
thanvigandhi_1
1
answer
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