Question

The function f(x) = 3x+cos 3x is

A. increasing on R

B. decreasing on R

C. strictly increasing on R

D. strictly decreasing on R

Answer 1

Given:

f(x) = 3x+cos3x

f’(x) = 3 - 3sin3x

f’(x) = 3(1- sin3x)

sin3x varies from [-1,1]

when sin3x is 1 f’(x) = 0 and sin3x is -1 f’(x) = 6

As the function is increasing in 0 to 6.

∴ The function is increasing on R.