Practicing Success

Target Exam

CUET

Subject

-- Mathematics - Section A

Chapter

Applications of Derivatives

Question:

The maximum value of x–x is

Options:

ee–1

\(e^\frac{1}{e}\)

\(e^\frac{-1}{e}\)

\(e^\frac{-4}{e}\)

Correct Answer:

\(e^\frac{1}{e}\)

Explanation:

f′(x) = x−x(−logx−1)

= −x−x(logx+1)

f′(x) = 0 when x = $\frac{1}{e}$​

f′(x) > 0 when 0 < x < $\frac{1}{e}$​

f′(x) < 0 when x > $\frac{1}{e}$​​

f(x) is maximum at x = $\frac{1}{e}$​

$f(\frac{1}{e}​)=(e)^{\frac{1}{e}}$