Examine the following functions for maxima and minima :
`f(x)=3x^(3)-9x^(2)-27x+15`

Examine the following functions for maxima and minima : f(x)=2x^(3)-21x^(2)+36x-20

Examine the following functions for maxima and minima : f(x)=x^(2)e^(x) .

Examine the following functions for maxima and minima : f(x)=x^(2)+(16)/(x^(2))

Examine the following functions for maxima and minima : Show that f(x)=x^(x) is minimum when x=(1)/(e) .

If f(x)=3x^(3)-9x^(2)-27x+15 , then

Prove that the following functions do not have maxima or minima : h(x)=x^(3)+x^(2)+x+1.

Prove that the following functions do not have maxima or minima: (c) h(x) = x^(3) + x^(2) + x + 1

Examine the following functions for maxima and minima : Find the maximum value of the function f(x)=x-e^(x) .

Find all the points of local maxima and minima of the f(x)=x^(3)-6x^(2)+9x-8