Prove that the function given by f (x) = x 3 3x 2 + 3x 100 is increasing in R.

Q18 of 168 Page 205

Prove that the function given by f (x) = x³ – 3x² + 3x – 100 is increasing in R.

We have, f (x) = x³ – 3x² + 3x – 100

=> f’(x) = 3x² -6x + 3

= 3(x² -2x + 1)

= 3(x-1)2

For any x ϵ R, (x -1)2 > 0

Thus, f’(x) is always positive in R.

Therefore, the given function (f) is increasing in R.

Prove that the function f given by f (x) = log sin x is strictly increasing on and strictly decreasing on .

Prove that the function f given by f (x) = log |cos x| is strictly decreasing onand strictly increasing on.

The interval in which y = x² e^–x is increasing is

Find the slope of the tangent to the curve y = 3x⁴ – 4x at x = 4.