Embibe Experts Solutions for Exercise 3: EXERCISE 6.3

The number of critical points of $f\left(x\right)=\frac{\left|x-1\right|}{x^2}$, in its domain, is

The function $f\left(x\right)=a\cos x+b\tan x+x$ has extreme values at $x=0$ and $x=\frac{\pi }{6}$, then

The greatest value of $f\left(x\right)=\cos \left(x{e}^{\left[x\right]}+7x^2-3x\right), x\in \left[-1, \infty \right)$ is

The greatest value of $f\left(x\right)={\left(x+1\right)}^{1/3}-{\left(x-1\right)}^{1/3}$ on $\left(-1, 1\right)$ is

The maximum value of the function $f\left(x\right)=\sin \left(x+\frac{\pi }{6}\right)+\cos \left(x+\frac{\pi }{6}\right)$ in the interval $\left(0,\frac{\pi }{2}\right)$ occurs at

The number of value(s) of $x,$ where the function $f\left(x\right)=\cos x+\cos \left(\sqrt{2}x\right)$ attains its maximum, is

Use differentiation to approximate ${\left(26\right)}^{\frac{1}{3}}$.

If the radius of a sphere is measured as $9 \mathrm{cm}$ with an error of $0.03 \mathrm{cm}$, then find the approximate error in calculating its volume.