The largest value of $f(x)=\frac{x^3}{3}

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Target Exam

CUET

Subject

-- Mathematics - Section A

Chapter

Applications of Derivatives

Question:

The largest value of $f(x)=\frac{x^3}{3}-abx$ occurs at x =

Options:

G.M. of a, b

A.M. of a, b

H.M. of a, b

None of these

Correct Answer:

G.M. of a, b

Explanation:

For $f(x)=\frac{x^3}{3}-abx$ to be least, we have $f'(x)=x^2-ab=0⇒x=\sqrt{ab}$

$f''(x) > 0$ for $x=\sqrt{ab}$

∴ f(x) has minimum at $x=\sqrt{ab}$ which is the G.M. of a, b