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Chain Rule, Log Differentiation & Rate of Change · Question 100 of 130

At which x is the slope of y = x^x zero?

Question 100

HardOriginal question

Let $y = x^{x}$ for $x > 0$ .

At which $x$ is the slope of $y = x^{x}$ zero?

0

Correct answerYour answer

e^{-1}

Correct answerYour answer

1

Correct answerYour answer

e

Correct answerYour answer

Show the answer and explanation

CorrectNot quiteAnswer B

Correct answer: B

$x^{x} > 0$ , so the slope is 0 exactly when $1 + \log x = 0$ .
$\log x = -1$ : $x = \frac{1}{e}$ .

Worth noting

$e$ solves $\log x = 1$ ; here it is $\log x = -1$ .

Concept: Where a logarithmic derivative vanishes
Typical timeTypical: 150 s
Your timeYours: —

The rule this testsLogarithmic differentiation

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