Practicing Success

Target Exam

CUET

Subject

-- Mathematics - Section A

Chapter

Applications of Derivatives

Question:

Let f(x) = $\left(4-x^2\right)^{2 / 3}$, then f has a

Options:

a local maxima at x = 0

a local maxima at x = 2

a local maxima at x = –2

none of these

Correct Answer:

a local maxima at x = 0

Explanation:

$f(x)=\left(4-x^2\right)^{2 / 3}$

$f'(x)=\frac{-4 x}{3\left(4-x^2\right)^{1 / 3}}=\frac{4 x}{3\left(x^2-4\right)^{1 / 3}}$

at x = –2   local minima

x = 0         local maxima

x = 2         local minima