Which is true of f(x) = x^3 + 2 on R?

Question 9

MediumOriginal question

Which is true of $f(x) = x^3 + 2$ on $\mathbb{R}$ ?

It has neither a maximum nor a minimum valueCorrect answerYour answerIts minimum value is 2Correct answerYour answerIts maximum value is 2Correct answerYour answerIt has a minimum value but no maximum valueCorrect answerYour answer

Show the answer and explanation

CorrectNot quiteAnswer A

Correct answer: A

As $x$ grows, $x^3$ grows without limit, and as $x$ falls, $x^3$ falls without limit.
So $x^3 + 2$ takes values above and below any number: there is no maximum and no minimum.

Worth noting

2 is $f(0)$ ; $f(-1) = 1$ is already smaller and $f(1) = 3$ larger.

Concept: A function with no maximum or minimum
Typical timeTypical: 90 s
Your timeYours: —

The rule this testsMaximum and minimum values

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Ten questions from Maxima & Minima, at your own pace.

Which is true of f(x)=x3+2f(x) = x^3 + 2f(x)=x3+2 on R\mathbb{R}R?

Explanation

Which is true of $f(x) = x^3 + 2$ on $\mathbb{R}$ ?