Question

Find the critical points for f (x) = (x – 2)2/3 (2x + 1).

Solution

Correct option is

(x = 1 & x = 2)

   

Clearly, f’(x) is not defined at x = 2, so, x = 2 is a critical point.

Another critical point is given by, 

                f’(x) = 0

SIMILAR QUESTIONS

Q1

Find the interval for which (x) = x – sin x is increasing or decreasing.

Q2

   

Where a is positive constant. Find the interval in which f’ (x) is increasing.

Q3

If a < 0, and f (x) = eax + e–ax is monotonically decreasing. Find the interval to which x belongs.   

Q5

If (x) = ax3 + bx2 + cx + d where abcd are real numbers and 3b2 < c2, is an increasing cubic function and g(x) = af’ (x) + bf’’ (x) + c2, then

Q6

If f : R  R, (x) is a differentiable bijective function, then which of the following is true?

Q7

If (x) and (x) are two positive and increasing function, then

Q8

If the function y = sin (f (x)) is monotonic for all values of x (where (x) is continuous), then the maximum value of the difference between the maximum and the minimum value of (x), is: 

Q9

 where 0 <x < π then the interval in which g(x) is decreasing is:   

Q10

 

Find all the values of a for which the function possess critical points.