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Application of Derivatives

Maxima and Minima

Premium Question

Grade 12

Question:

The function $f(x) = x^x$ ($x > 0$) has a stationary point at:

(1) $x = e$

(2) $x = \frac{1}{e}$

(3) $x = 1$

(4) $x = e^2$

Step-by-Step Solution

Key Concept: Take logarithms of $y = x^x$ to write $\ln y = x \ln x$, differentiate implicitly, and set $dy/dx = 0$.

The detailed step-by-step mathematical proof is available inside the Mathbee app workspace.

Correct Answer: (2)