Recent questions in Application of Derivatives

Find the equations of the tangent and normal to the given curves at the indicated points: $ (v) \: x = \cos t,y=\sin t\; at \;(t=\large\frac{\pi}{4})$

asked Jul 11, 2013 by sreemathi.v

1 answer

Find the equations of the tangent and normal to the given curves at the indicated points: $ (iv) \: y = x^2\; at \;(0, 0)$

asked Jul 11, 2013 by sreemathi.v

1 answer

Find the equations of the tangent and normal to the given curves at the indicated points: $ (iii) \: y = x^3\; at \;(1, 1)$

asked Jul 11, 2013 by sreemathi.v

1 answer

Find the equations of the tangent and normal to the given curves at the indicated points: $ (ii) \: y = x^4 - 6x^3 + 13x^2 - 10x + 5\; at \;(1, 3)$

asked Jul 11, 2013 by sreemathi.v

1 answer

Find points on the curve$ \large\frac{x^2}{9} + \frac{y^2}{16} = 1$ at which the tangents are $(ii)\; parallel\; to\; y - axis$

asked Jul 11, 2013 by sreemathi.v

1 answer

Find the intervals in which the following functions are strictly increasing or decreasing: $(e) \;(x+1)^3(x-3)^3$

asked Jul 9, 2013 by sreemathi.v

1 answer

Find the intervals in which the following functions are strictly increasing or decreasing: $(d) \;6-9x-x^2$

asked Jul 9, 2013 by sreemathi.v

1 answer

Find the intervals in which the following functions are strictly increasing or decreasing: $(c) \;-2x^3-9x^2-12x+1$

asked Jul 9, 2013 by sreemathi.v

1 answer

Find the intervals in which the following functions are strictly increasing or decreasing: $(b) \;10-6x-2x^2$

asked Jul 9, 2013 by sreemathi.v

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 rates of change of (b) the area of the triangle.

asked Jul 5, 2013 by sreemathi.v

1 answer

Find the rate of change of the area of a circle with respect to its radius r when $(b)\; r = 4 cm$

asked Jul 5, 2013 by sreemathi.v

1 answer

Find the maximum profit that a company can make if the profit function is given by \[P(x)=41-24x-18x^2\]

asked Jan 30, 2013 by meena.p

1 answer

Find the sides of a rectangle of greatest area that can be inscribed in the ellipse $ x^2+4y^2=16$

asked Jan 30, 2013 by meena.p

1 answer

A poster is to contain $50cm^2$ of matter with borders of 4 cm at top and bottom and of 2 cm on each side. Find the dimensions if the total area of the poster is minimum.

asked Jan 30, 2013 by meena.p

1 answer

Two equal sides of an isosceles triangle with fixed base b are decreasing at the rate of 3cm/sec. How fast is the area decreasing when the two equal sides are equal to the base?

asked Jan 30, 2013 by meena.p

1 answer

Find the local maximum and local minimum value of the function. \[f(x)=\sin x+\frac{1}{2}\cos 2x\;in\;[0,\pi/2]\]

asked Jan 30, 2013 by meena.p

1 answer

Find two positive numbers x and y such that their sum is 16 and sum of whose cubes is minimum.

asked Jan 30, 2013 by meena.p

1 answer

Find the interval in which $ y=x^2e^{-x}$ is increasing.

asked Jan 30, 2013 by meena.p

1 answer

Find the intervals in which f(x) = logcosx is strictly decreasing and strictly increasing.

asked Jan 30, 2013 by meena.p

1 answer

At what point in the interval $ [0,2\pi] $ does the function $\sin2x$ attain its maximum value?

asked Jan 30, 2013 by meena.p

1 answer

FInd whether $ f(x)=e^x$ has maxima or minima.

asked Jan 30, 2013 by meena.p

1 answer

Without using derivatives find the maximum and minimum value of $ f(x) = \sin2x+7 $

asked Jan 30, 2013 by meena.p

1 answer

Without using derivatives find the maximum or minimum value of $ f(x)=-| x+5 |+3$

asked Jan 30, 2013 by meena.p

0 answers

Find the maxima or minima if any of the function $f(x)=\Large\frac{1}{x^2+2}$

asked Jan 30, 2013 by meena.p

0 answers

FInd the local maxima and local minima if any of the function $f(x)=e^{5x}$

asked Jan 30, 2013 by meena.p

0 answers

The curve $ y=ax^3+6x^2+bx+5$ touches the x-axis at P(-2,0) and cuts the y-axis at a point Q where its gradient is 3. Find a,b,c.

asked Jan 30, 2013 by meena.p

0 answers

Find the maximum and minimum value of $ f(x)=| (\sin 4x+5) |$ without using derivatives.

asked Jan 30, 2013 by meena.p

0 answers

Find the maximum and minimum values of 'f', if any of the function $ f(x) = | x |,x \in R$

asked Jan 30, 2013 by meena.p

0 answers

Find the approximate value of $ 2x^4-160=0 $

asked Jan 30, 2013 by meena.p

0 answers

Using differentials evaluate $\tan 44^\circ approximately, 1^\circ=0.07145^\circ$

asked Jan 30, 2013 by meena.p

0 answers

Use differentials to evaluate $ \bigg(\large\frac{17}{81}\bigg)^{1/4}$ approximately.

asked Jan 30, 2013 by meena.p

0 answers

Find the appropriate change in volume of a cube when side increases by 1%.

asked Jan 30, 2013 by meena.p

0 answers

If $ y=x^4-10 $ and if x changes from 2 to 1.97, what is the appropriate change in y ?

asked Jan 30, 2013 by meena.p

0 answers

Using differentials find the appropriate value of $(82)^{1/4}$

asked Jan 30, 2013 by meena.p

0 answers

Find the angle between the parabolas $ y^2=4ax\;and\;x^2=4by$ at their point of intersection other than the origin.

asked Jan 30, 2013 by meena.p

0 answers

FInd the equation of the tangent to the curve $\sqrt x+ \sqrt y =a$ at the point $\bigg(\large\frac{a^2}{4},\frac{a^2}{4}\bigg)$

asked Jan 30, 2013 by meena.p

0 answers

FInd the equation of tangent and normal to the curve $ y^2=\large\frac{x^3}{4-x}$ at (2,-2)

asked Jan 30, 2013 by meena.p

0 answers

Find the equations of the normal lines to the curve $ y=4x^3-3x+5$ which are parallel to the line $9y+x+3=0$

asked Jan 30, 2013 by meena.p

0 answers

Find equation of tangents to the curve $ x=a\cos ^3 \theta,y=b\sin ^3 \theta $ at $\theta=\pi/4$

asked Jan 30, 2013 by meena.p

0 answers

Find the points on the curve $\large\frac{x^2}{4}+\frac{y^2}{25}=1$ at which the tangents are parallel to x-axis and parallel to y-axis.

asked Jan 30, 2013 by meena.p

0 answers

Find the interval on which the function $ \large\frac{x}{log x}$ is increasing or decreasing.

asked Jan 29, 2013 by meena.p

0 answers

FInd the interval in which $f(x)=8+36x+3x^2-2x^3$ is increasing or decreasing.

asked Jan 29, 2013 by meena.p

0 answers

Find the interval in[0,2\pi] in which the function $ \Large\frac{-4.\sin x+2x+x \cos x}{2+\cos x}$ is increasing or decreasing.

asked Jan 29, 2013 by meena.p

0 answers

Find whether $ f(x)=\cos (2x+\pi/4)\:is\:increasing\:or\:decreasing\:in\:(\frac{3\pi}{8},\frac{5\pi}{8})$ .

asked Jan 29, 2013 by meena.p

0 answers

Find the interval in which the function $f(x)=x^4-4x^3+4x^2+15$ is increasing or decreasing.

asked Jan 29, 2013 by meena.p

0 answers

Show that $ f(x)=3x^5+40x^3+240x$ is always increasing on R.

asked Jan 29, 2013 by meena.p

0 answers

Show that the function $f(x)=e^{2x}$ is strictly increasing on R.

asked Jan 29, 2013 by meena.p

0 answers

Water is passed into an inverted cone of base radius 5 cm and depth 10 cm at the rate of $\Large\frac{3}{2}$ c.c/sec. Find the rate at which the level of water is rising when depth is 4 cm.

asked Jan 29, 2013 by meena.p

0 answers

Gas is escaping from a spherical balloon at the rate of $900 cm^3$/sec. How fast is the surface area, radius of the balloon shrinking when the radius of the balloon is 30cm?

asked Jan 29, 2013 by meena.p

0 answers

The surface area of a spherical bubble is increasing at the rate of $ 2 cm^2$/sec. Find the rate at which the volume of the bubble is increasing at the instant if its radius is 6 cm.

asked Jan 29, 2013 by meena.p

0 answers

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