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: (c) h(x) = x^(3) + x^(2) + x + 1

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

Differentiate the following functions w.r.t x using first principle. f(x) = e^(2x)

Examine the following functions for continuity: (a) f(x) = x - 5

Examine the following functions for continuity: (d) f(x) = |x - 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: (i) f(x = x^(2))

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: (vi) g(x) = x/2 + 2/x, x gt 0

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: (ii) g(x) = x^(3) - 3x

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: (iv) f(x) = sin x - cos x, 0 lt x lt 2 pi