The total number of local maxima and local minima of the function f (x) = {(2 + x)³, when - 3 < x ≤ -1 and x^2/3, when -1 < x < 2 is

1) 0

2) 1

3) 2

4) 3

Solution: (3) 2

f (x) = {(2 + x)³, when – 3 < x ≤ -1 and x^2/3, when -1 < x < 2

f’ (x) = f (x) = {3 (2 + x)², when – 3 < x ≤ -1 and (2 / 3) x^-1/3, when -1 < x < 2

For – 3 < x ≤ – 1, f’ (x) > 0.

But – 1 < x < 0, f’ (x) < 0.

One local maximum at x = -1 and further for 0 < x < 2, f’ (x) > 0.