Embibe Experts Solutions for Chapter: Application of Derivatives, Exercise 1: BITSAT 2017

If $f$ and $g$ are differentiable function in $\left[0,1\right]$ satisfying $f\left(0\right)=2=g\left(1\right), g\left(0\right)=0$ and $f\left(1\right)=6$, then for some $c\in \left(0,1\right)$

The least value of the function $f\left(x\right)={\int }_0^x\left(3\sin x+4\cos x\right)dx$ in the interval $\left[\frac{5\pi }{4},\frac{4\pi }{3}\right]$ is

The difference of maximum and minimum values of $f\left(x\right)=x^2{e}^{-x}$ is

The distance between the origin and the normal to curve $y=e^{2x}+x^2$ at $x=0$ is

An inverted conical flask is being filled with water at the rate of $3 {\mathrm{cm}}^3 {\sec }^{-1}$. The height of the flask is $10 \mathrm{cm}$ and the radius of the base is $5 \mathrm{cm}$. How fast is the water level rising when the level is $4 \mathrm{cm}?$

For which interval the given function $f\left(x\right)=-2x^3-9x^2-12x+1$ is decreasing?

If the curve $y=a^x$ and $y=b^x$ intersect at angle $\alpha$, then $\tan \alpha$ is equal to

The maximum value of $f\left(x\right)=x+\sin 2x,x\in [0,2\pi ]$ is