Question

The total number of local maxima and local minima of the function 

f(x) = (2 + x)³, -3 < x ≤ -1

f(x) = x²/3,, -1 < x < 2

is

(a) 0

(b) 1

(c) 2

(d) 3

Answer 1

Correct option (c) 2

Explanation :

Clearly, f'(x) changes its sign at x = -1 from +ve to -ve and so f(x ) has local maxima at x = -1.

Also, f'(0) does not exist but f'(0^-) < 0 and f'(0⁺) < 0. It can only be inferred that f(x) has a possibility of a minima at x = 0.

Hence, the given function has one local maxima at x = -1 and one local minima at x = 0