Recent questions and answers in Differential Calculus Applications - I - Clay6.com, a Free resource for your JEE, AIPMT and Board Exam preparation

Find the dimensions of the rectangle of largest area that can be inscribed in a circle of radius $r$.

answered Apr 29, 2014 by meena.p

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Find the intervals of concavity and the points of inflection of the following functions: $y=12x^{2}-2x^{3}-x^{4}$

answered Aug 5, 2013 by meena.p

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Find the intervals of concavity and the points of inflection of the following functions: $f(\theta)=\sin 2\theta $ in $ (0 , \pi )$

answered Aug 5, 2013 by meena.p

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Find the intervals of concavity and the points of inflection of the following functions: $f(x)=x^{4}-6x^{2}$

answered Aug 5, 2013 by meena.p

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Find the intervals of concavity and the points of inflection of the following functions: $f(x)=2x^{3}+5x^{2}-4x$

answered Aug 5, 2013 by meena.p

1 answer

Find the intervals of concavity and the points of inflection of the following functions: $f(x)=x^{2}-x$

answered Aug 5, 2013 by meena.p

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Resistance to motion,$F$, of a moving vehicle is given by,$F=\large\frac{5}{x}$$+100x.$ Determine the minimum value of resistance.

answered Aug 5, 2013 by meena.p

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Show that of all the rectangles with a given perimeter the one with the greatest area is a square.

answered Aug 5, 2013 by meena.p

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Show that of all the rectangles with a given area the one with smallest perimeter is a square.

answered Aug 1, 2013 by meena.p

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Find two positive numbers whose product is $100$ and whose sum is minimum.

answered Aug 1, 2013 by meena.p

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Find two numbers whose sum is $100 $ and whose product is a maximum.

answered Aug 1, 2013 by meena.p

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Find the local maximum and minimum values of the following: $t+ \cos t$

answered Aug 1, 2013 by meena.p

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Find the local maximum and minimum values of the following: $\sin^{2} \theta , [0 ,\pi ]$

answered Aug 1, 2013 by meena.p

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Find the local maximum and minimum values of the following: $(x^{2}-1)^{3}$

answered Aug 1, 2013 by meena.p

1 answer

Find the local maximum and minimum values of the following: $x^{4}-6x^{2}$

answered Aug 1, 2013 by meena.p

1 answer

Find the local maximum and minimum values of the following: $2x^{3}+5x^{2}-4x $

answered Aug 1, 2013 by meena.p

1 answer

Find the local maximum and minimum values of the following: $x^{3}-x$

answered Aug 1, 2013 by meena.p

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Find the absolute maximum and absolute minimum values of $f$ on the given interval: $\;f(x)=x-2\cos x , [-\pi ,\pi ]$

answered Jul 31, 2013 by meena.p

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Find the absolute maximum and absolute minimum values of $f$ on the given interval: $\;f(x)=\sin x +\cos x ,[0 ,\large\frac {\pi}{3}]$

answered Jul 31, 2013 by meena.p

1 answer

Find the absolute maximum and absolute minimum values of $f$ on the given interval: $\;f(x)=\large\frac{x}{x+1},$$ [1 , 2 ]$

answered Jul 31, 2013 by meena.p

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Find the absolute maximum and absolute minimum values of $f$ on the given interval: $\;f(x)=\sqrt{9-x^{2}} ,[-1 , 2]$

answered Jul 31, 2013 by meena.p

1 answer

Find the intervals on which $f$ is increasing or decreasing. $f(x)=x-2\sin x,[0 , 2\pi ]$

answered Jul 31, 2013 by meena.p

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Find the absolute maximum and absolute minimum values of $f$ on the given interval: $\;f(x)=x^{3}-12x+1 ,[-3 , 5]$

answered Jul 31, 2013 by meena.p

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Find the absolute maximum and absolute minimum values of $f$ on the given interval: $\;f(x)=1-2x-x^{2}, [-4 , 1 ]$

answered Jul 31, 2013 by meena.p

1 answer

Find the absolute maximum and absolute minimum values of $f$ on the given interval: $\;f(x)=x^{2}-2x+2 , [0 , 3 ]$

answered Jul 31, 2013 by meena.p

1 answer

Find the critical numbers and stationary points of each of the following functions.$\;f(\theta)=\theta+\sin\theta$ in $[0 , 2\pi ]$

answered Jul 31, 2013 by meena.p

1 answer

Find the critical numbers and stationary points of each of the following functions. $\;f(\theta)=\sin^{2} 2\theta \;$in$\;[0 , \pi ]$

answered Jul 31, 2013 by meena.p

1 answer

Find the critical numbers and stationary points of each of the following functions.$\;f(x)=\large\frac{x+1}{x^{2}+x+1}$

answered Jul 31, 2013 by meena.p

1 answer

Find the critical numbers and stationary points of each of the following functions.$\;f(x)=x^{3}-3x+1$

answered Jul 31, 2013 by meena.p

1 answer