Tamil Nadu Board Solutions for Chapter: Applications of Differential Calculus, Exercise 7: Exercise 7

Find intervals of concavity and points of inflection for the following function : $f\left(x\right)=x(x-4{)}^3$

Find intervals of concavity and points of inflection for the following function :

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

Find intervals of concavity and points of inflection for the following function :

$f\left(x\right)=\frac{1}{2}(e^x-e^{-x})$

Find the local extrema for the following functions using second derivative test: 

$f\left(x\right)=-3x^5+5x^3$

Find the local extrema for the following functions using second derivative test: 

$f\left(x\right)=x\log x$

Find the local extrema for the following functions using second derivative test: $f\left(x\right)=x^2{e}^{-2x}$

For the function $f\left(x\right)=4x^3+3x^2-6x+1$ find the intervals of monotonicity, local extrema, intervals of concavity and points of inflection.