The function $f$ defined by $f\left(x\right)=x^3-3x^2+5x+7$ is:

Important Questions on Application of Derivatives

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 27 - Application of Derivatives>JEE Main - 9th April 2016>Q 89

The minimum distance of a point on the curve $y=x^2-4$ from the origin is 

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 27 - Application of Derivatives>JEE Main - 9th April 2016>Q 90

If the tangent at a point $\mathrm{P}$, with parameter $t$, on the curve $x=4t^2+3, y=8t^3-1, t \in R,$ meets the curve again at a point $\mathrm{Q}$, then the coordinates of $\mathrm{Q}$ are :

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 27 - Application of Derivatives>JEE Main - 3rd April 2016>Q 91

Consider $f\left(x\right)={\tan }^{-1}\left(\sqrt{\frac{1+\sin x}{1-\sin x}}\right), x \in \left(0,\frac{\pi }{2}\right).$ A normal to $y=f\left(x\right)$ at $x=\frac{\pi }{6}$ also passes through the point

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 27 - Application of Derivatives>JEE Main - 3rd April 2016>Q 92

A wire of length $2$ units is cut into two parts which are bent respectively to form a square of side $=x$ units and a circle of radius $=r$ units. If the sum of the areas of the square and the circle so formed is minimum, then

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 27 - Application of Derivatives>JEE Main - 10th April 2016>Q 93

Let C be a curve given by $y\left(x\right)=1+ \sqrt{4x-3}$,$x>\frac{3}{4}$. If $P$ is a point on C, such that the tangent at $P$ has slope $\frac{2}{3}$, then a point through which the normal at $P$ passes, is :

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 27 - Application of Derivatives>JEE Main - 10th April 2016>Q 94

Let $f\left(x\right)={\sin }^{4}x+{\cos }^{4}x.$ Then, $f$ is an increasing function in the interval:

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 27 - Application of Derivatives>JEE Main - 10th April 2015>Q 95

The distance from the origin, of the normal to the curve, $x=2\cos t+2t\sin t, y=2\sin t-2t\cos t at t=\frac{\pi }{4},$ is :

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 27 - Application of Derivatives>JEE Main - 11th April 2015>Q 96

From the top of a $64$ metres high tower, a stone is thrown upwards vertically with the velocity of $48 \mathrm{m}/\mathrm{s}.$ The greatest height (in metres) attained by the stone, assuming the value of the gravitational acceleration $g=32 \mathrm{m}/{\mathrm{s}}^2$, is: