Show that the following functions do not have any local extremun
(iii) `f(x) = 1+x+x^2+x^3`

Show that the following functions do not have any local extremun (i) f(x) = e^x

Show that the following functions do not have any local extremun (ii) f(x) = log_ex

Show that the following functions do not have any local extremun (iv) f(x) = x^3-3x^2+15x+2

Show that the function f(x)=3x+2 is one-one and onto.

Examine the continuity of the following function at the given point : f(x) = {(1 + x, x 0),(1, x = 0):} at x = 0.

Examine the continuity of the following function at the given point : f(x) = {(x^2 - 2x + 3, x 1):} x = 1.

Examine the continuity of the following function at the given point : f(x) ={((3/2-x, 1/2 le x < 1)),((3/2, x = 1)),((3/2 + x, 1 < x le 2)):} at x = 1.

Find the range of the following functions given by : f(x)=|x-3|

Find the domain of the following functions given by f(x)=x|x| .

Find the domain of the following functions given by f(x)=1/sqrt(2-x)(x-3)