Embibe Experts Solutions for Chapter: Applications of Differential Calculus, Exercise 1: Exercise

A missile fired from ground level rises $x$ metres vertically upwards in $t$ seconds and $x=100\mathrm{t}-\frac{25}{2}{\mathrm{t}}^2$. Find : the velocity with which the missile strikes the ground.

If $w=x+2y+z^2$ and $x=\cos t; y=\sin t; z=t$ find $\frac{dw}{dt}$ by using chain rule. Also find $\frac{dw}{dt}$ by substitution of $x, y$ and $z$ in $w$ and hence verify the result.

Find the equations of the tangent and normal to the parabola $y^2=8x\text{ at }t=\frac{1}{2}$.

Let $P$ be a point on the curve $y=x^3$ and suppose that the tangent line at $P$ intersects the curve again at $Q$. Prove that the slope at $Q$ is four times the slope at $P$.

If $f\left(x\right) \text{and} g\left(x\right)$ are two functions as defined in Generalised law of mean then LaGrange's law of mean is a particular case of Generalised law of mean for:

Verify Rolle’s theorem for the function $f\left(x\right)=\left|x-2\right|+\left|x-5\right|$ in $[1, 6]$.

The surface area of a sphere when the volume is increasing at the same rate as its radius, is :

Which one of the following statements is true about the curve $y=x^{\frac{1}{3}}$?