Tamil Nadu Board Solutions for Chapter: Applications of Differential Calculus, Exercise 6: Exercise 6

Find the absolute extrema of the following function on the given closed interval.

$f\left(x\right)=3x^4-4x^{3 }; [-1,2]$

Find the absolute extrema of the following function on the given closed interval.

$f\left(x\right)=6x^{\frac{4}{3}}-3x^{\frac{1}{3}} ; \left[-1,1\right]$

Find the absolute extrema of the following function on the given closed interval.

$f\left(x\right)=2\cos x+\sin 2x ; \left[0,\frac{\mathrm{\pi }}{2}\right]$

Find the intervals of monotonicities and hence find the local extrema for the following function:

$f\left(x\right)=2x^3+3x^2-12x$

Find the intervals of monotonicities and hence find the local extrema for the following function:

$f\left(x\right)=\frac{x}{x-5}$

Find the intervals of monotonicities and hence find the local extrema for the following function:

$f\left(x\right)=\frac{e^x}{1-e^x}$

Find the intervals of monotonicities and hence find the local extrema for the following function:

$f\left(x\right)=\frac{x^3}{3}-\log x$

Find the intervals of monotonicities and hence find the local extrema for the following function:

$f\left(x\right)=\sin x\cos x+5,x\in \left(0,2\mathrm{\pi }\right)$