The total number of local maxima and local minima of the function f(x)= begincases(2+x)3, -3

Question

The total number of local maxima and local minima of the function f(x)= begincases(2+x)3, -3 < x ≤-1 x2 / 3, -1 < x < 2 endcases is (A) 0 (B) 1 (C) 2 (D) 3

Tardigrade Admin · Accepted Answer

Local maximum at x =-1 and local minimum at x =0 Hence total number of local maxima and local minima is 2 . <img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/mathematics/61bb4a84ad91b7f66785fc2b3db766d4-.png" />

Q. The total number of local maxima and local minima of the function
$f (x) = {(2 + x)^{3}, x^{2/3}, - 3 < x \leq - 1 - 1 < x < 2$ is

0

1

2

3

Local maximum at $x = - 1$
and local minimum at $x = 0$
Hence total number of local maxima and local minima is $2.$

Q. The total number of local maxima and local minima of the function f(x)={(2+x)3,x2/3,​−3<x≤−1−1<x<2​ is

0

1

2

3

Local maximum at x=−1 and local minimum at x=0 Hence total number of local maxima and local minima is 2.

Q. The total number of local maxima and local minima of the function
$f (x) = {(2 + x)^{3}, x^{2/3}, - 3 < x \leq - 1 - 1 < x < 2$ is

Local maximum at $x = - 1$
and local minimum at $x = 0$
Hence total number of local maxima and local minima is $2.$