EXERCISE-4

Find the interval of monotonicity for the function $f\left(x\right)=2e^{x^2-4x}$ and represents on the number line.

Find the interval of monotonicity for the function $f\left(x\right)=\frac{e^x}{x}$ and represents on the number line.

Find the interval of monotonicity for the function $f\left(x\right)=x^2{e}^{-x}$ and represents on the number line.

Find the points of local maxima/minima of following function:

$f\left(x\right)=-{\left(x-1\right)}^3{\left(x+1\right)}^2$

Find the points of local maxima/minima of following function:

$y=\frac{3x^2+4x+4}{x^2+x+1}$

Find the points on the curve $a{x}^2+2bxy+a{y}^2=c; c>b>a>0$, whose distance from the origin is minimum.

The perpendicular from the origin to the tangent at any point on a curve is equal to the abscissa of the point of contact. Find the equation of the curve satisfying the above condition and which passes through $\left(1,1\right)$.

Use differentials to find the approximate value of  $\sqrt[3]{26}$.