Embibe Experts Solutions for Chapter: Application of Derivatives, Exercise 1: EXERCISE

A man is moving away from a tower $41.6 \mathrm{m}$ high at a rate of $2 \mathrm{m}/\mathrm{s}$. If the eye level of the man is $1.6 \mathrm{m}$ above the ground, then the rate at which the angle of elevation of the top of the tower changes, when he is at a distance of $30 \mathrm{m}$ from the foot of the tower, is

Suppose that $f$ is differentiable for all $x$ and that $f^{\text{'}}\left(x\right)\le 2$ for all $x.$ If $f\left(1\right)=2$ and $f\left(4\right)=8,$ then $f\left(2\right)$ has the value equal to

The radius of a right circular cylinder increases at the rate of $0.1 \mathrm{cm}/\min ,$ and the height decreases at the rate of $0.2 \mathrm{cm}/\min .$ The rate of change of the volume of the cylinder, in ${\mathrm{cm}}^3/\min .$, when the radius is $2 \mathrm{cm}$ and the height is $3 \mathrm{cm}$ is

A cube of ice melts without changing its shape at the uniform rate of $4 {\mathrm{cm}}^3/\min .$ The rate of change of the surface area of the cube, in ${\mathrm{cm}}^2/\min ,$ when the volume of the cube is $125 {\mathrm{cm}}^3,$ is

Let $f^{\text{'}}\left(x\right)=e^{x^2}$ and $f\left(0\right)=10 .$ If $A<f\left(1\right)<B$ can be concluded from the mean value theorem, then the largest value of $(A-B)$ equals

If $f$ be a continuous function on $[0,1],$ differentiable in $(0,1)$ such that $f\left(1\right)=0,$ then there exists some $c\in (0,1)$ such that

Given $g\left(x\right)=\frac{x+2}{x-1}$ and the line $3x+y-10=0,$ then the line is

If $f\left(x\right)$ and $g\left(x\right)$ are differentiable functions for $0\le x\le 1$ such that $f\left(0\right)=10, g\left(0\right)=2, f\left(1\right)=2, g\left(1\right)=4,$ then in the interval $(0,1)$