Assertion (A): f(x) = x^3 is strictly increasing on R. Reason (R): f'(x) > 0 for every real x when f(x) = x^3.

Increasing & Decreasing Functions · Question 19 of 74

Question 19

MediumOriginal question

Assertion (A): $f(x) = x^3$ is strictly increasing on $\mathbb{R}$ .
Reason (R): $f'(x) > 0$ for every real $x$ when $f(x) = x^3$ .

Both A and R are true, and R is the correct explanation of A.Correct answerYour answerBoth A and R are true, but R is not the correct explanation of A.Correct answerYour answerA is true, but R is false.Correct answerYour answerA is false, but R is true.Correct answerYour answer

Show the answer and explanation

CorrectNot quiteAnswer C

Correct answer: C

For $x_1 < x_2$ , $x_1^3 < x_2^3$ , so A is true.
But $f'(0) = 0$ , so R is false: a function can be strictly increasing with its derivative 0 at a single point.

Concept: Strictly increasing with a zero derivative
Typical timeTypical: 90 s
Your timeYours: —

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Assertion (A): f(x)=x3f(x) = x^3f(x)=x3 is strictly increasing on R\mathbb{R}R.Reason (R): f′(x)>0f'(x) > 0f′(x)>0 for every real xxx when f(x)=x3f(x) = x^3f(x)=x3.

Explanation

Assertion (A): $f(x) = x^3$ is strictly increasing on $\mathbb{R}$ .
Reason (R): $f'(x) > 0$ for every real $x$ when $f(x) = x^3$ .