Which describes $f(x) = x^{3} - 6 x^{2} + 12 x + 5$ ?

Strictly decreasing on

\mathbb{R}

Correct answerYour answerIncreasing on one part of

\mathbb{R}

and decreasing on anotherCorrect answerYour answerConstant on

\mathbb{R}

Correct answerYour answerStrictly increasing on

\mathbb{R}

Correct answerYour answer

Show the answer and explanation

CorrectNot quiteAnswer D

Correct answer: D

$f'(x) = 3 \left(x - 2\right)^{2}$ .
Here $3(x - 2)^2 \ge 0$ , and it is 0 only at the single point $x = 2$ , so $f$ is strictly increasing on $\mathbb{R}$ .

Worth noting

A derivative that is 0 at a single point, with the same sign on both sides, does not stop a function from strictly increasing.

Ten questions from Increasing & Decreasing Functions, at your own pace.

Which describes f(x)=x3−6x2+12x+5f(x) = x^{3} - 6 x^{2} + 12 x + 5f(x)=x3−6x2+12x+5?