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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.\[(a)\;(1,2)\qquad(b)\;(2,3)\qquad(c)\;(5/2,3)\qquad(d)\;(2,4)\]
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If the line ax+by+c = 0 is normal to the curve xy = 1 then \[(a)\;a>0,b>0 \qquad (b)\;a<0,b<0 \qquad(c)\;a<0,b>0\qquad(d)\;a<0,b<0.\]
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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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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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application of derivatives
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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?
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Jan 20, 2014
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question no. 25 of exercise 6.5
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SHOW THAT THE SEMI VERTICAL ANGLE OF THE CONE OF THE MAXIMUM VOLUME AND OF GIVEN SLANT HEIGHT IS
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question no. 25 of exercise 6.5
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question no. 25 of exercise 6.5
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question no. 25 of exercise 6.5
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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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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?
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Dec 23, 2013
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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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Dec 22, 2013
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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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Find the maximum value of \(2x^3 – 24x + 107\) in the interval \([1, 3]\).
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Find the intervals in which the function $f$ given by $f (x) = 2x^2 - 3x$ is $(a) \;strictly\; increasing$
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The interval on which the function $f(x)=2x^3+9x^2+12x-1$ is decreasing is :
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Two curves $x^3-3xy^2+2=0$ and $3x^2-y^3-2=0$ intersect at an angle of
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The least value of the function $f(x)=ax+\frac{b}{x}(a>0,b>0,x>0)$ is ___________.
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Aug 13, 2013
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The function $f(x)=\Large\frac{2x^2-1}{x^4}$,x>0,decreases in the interval__________.
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The value of a for which the function $f(x)=sin x-ax+b$ increases on R are__________.
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Aug 13, 2013
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1
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The equation of normal to the curve y=tan x at (0,0) is___________.
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Aug 13, 2013
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The curves $y=4x^2+2x-8$ and $y=x^3-x+13$ touch each other at the point_________.
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Aug 13, 2013
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1
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The maximum value of $\Large\frac{1}{x}$ is:
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Aug 13, 2013
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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
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Aug 13, 2013
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Choose the correct answer in the normal to the curve \(x^2 = 4y\) passing \((1,2)\) is
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class12
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ch6
misc
q23
p244
sec-c
medium
math
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Aug 13, 2013
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1
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Choose the correct answer in the normal at the point \((1,1)\) on the curve \(2y + x^2 = 3\) is
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class12
bookproblem
ch6
misc
q22
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medium
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Aug 13, 2013
by
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1
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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
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class12
bookproblem
ch6
misc
q21
p244
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Aug 13, 2013
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sreemathi.v
1
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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
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class12
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ch6
misc
q20
p243
sec-b
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Aug 13, 2013
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sreemathi.v
1
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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
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Aug 13, 2013
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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}$$\pi h^3 \: tan^2 \: \alpha $
cbse
class12
bookproblem
ch6
misc
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p243
sec-c
medium
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Aug 13, 2013
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sreemathi.v
1
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$f(x)=x^x$ has a stationary point at
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class12
ch6
q58
p141
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exemplar
sec-a
difficult
math
answered
Aug 12, 2013
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1
answer
Maximum slope of the curve $y=x^3+3x^2+9x-27$ is
cbse
class12
ch6
q57
p141
objective
exemplar
sec-a
medium
math
answered
Aug 12, 2013
by
thanvigandhi_1
1
answer
At $x=\Large\frac{5}{6}$$,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 \((a, b).\)
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class12
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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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