For all real values of x, increasing function f(x) is:

Question

For all real values of x, increasing function f(x) is: (A) x-1 (B) x3 (C) x2 (D) x4

Tardigrade Admin · Accepted Answer

Note: A function f (x) is s.t.b increasing function if f '(x) > 0
(i) Now, if f (x) =

\frac{1}{x} \Rightarrow f^{'} (x) = \frac{- 1}{x ^{2}}

the function becomes decreasing for x > 0
(ii) For,

f (x) = x^{3} \Rightarrow f^{'} (x) = 3 x^{2}

3 x^{2}

is always > 0 for any real value of x
(iii) For

f (x) = x^{2} \Rightarrow f^{'} (x) = 2 x

which clearly shows that f (x) is a decreasing function for x < 0

Q. For all real values of x, increasing function f(x) is: