Embibe Experts Solutions for Chapter: Application of Derivatives, Exercise 1: Assam Board-2018

Find the maximum and minimum values of the function $f\left(x\right)=x+\sin 2x$ on $[0,2\pi ]$

Prove that the area of right-angled triangle of given hypotenuse is maximum when the triangle is isosceles.

Find the equation of the tangent to the curve $y=f\left(x\right)$ at $\left(x_0,y_0\right)$, if $\frac{dy}{dx}$ does not exist at this point.

If $f\left(x\right)=x^3-6x^2-36x+7$, find the interval for which $f\left(x\right)$ is strictly increasing.

If $f\left(x\right)=x^3-6x^2-36x+7$, find the interval for which $f\left(x\right)$ is strictly decreasing.

Find the area of the largest rectangle that can be formed having a perimeter of $40$ meters.

Prove that the curves $x=y^2$ and $xy=k$ cut at right angles if $8k^2=1$.

Find the absolute maximum and minimum values of the function $f$ given by $f\left(x\right)=\mathrm{c}\mathrm{o}{\mathrm{s}}^{2}x+\mathrm{s}\mathrm{i}\mathrm{n}x,x\in \left[0,\pi \right]$.