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

Prove that the following functions do not have maxima or minima: (a) f(x) = e^(x)

Prove that the following functions do not have maxima or minima: (b) g(x) = log x

Examine the following functions for continuity: (c) f(x) = (x^(2) - 25)/(x +5), x != -5

Find all the points of local maxima and local minima of the function f given by f(x) = 2x^( 3) – 6x^(2) + 6x +5.

Find the local maxima and local minima. If any of the following function. Also, find the local maximum and the local minimum values, as the case may be as follows: (v) f(x) = x^(3) - 6x^(2) + 9x + 15

Using Division Algorithm prove that the polynomial g(x) = x^(2) + 3x + 1 is a factor of f(x) = 3 x^(4) + 5 x^(3) - 7 x^(2) + 2x + 2

Which of the following function from Z to itself are bijections? f(x)=x^3 (b) f(x)=x+2 f(x)=2x+1 (d) f(x)=x^2+x

Prove that the function defined by f(x)= tan x is a continuous function.

Find all points of local maxima and local minima of the function f given by f(x) = x^(3) – 3x + 3.