Assertion (A): f(x) = x^3 + kx is strictly increasing on R for every k > 0. Reason (R): When k > 0, f'(x) = 3x^2 + k > 0 for every real x.

Question 72

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Assertion (A): $f(x) = x^3 + kx$ is strictly increasing on $\mathbb{R}$ for every $k > 0$ .
Reason (R): When $k > 0$ , $f'(x) = 3x^2 + k > 0$ for every real $x$ .

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 A

Correct answer: A

R: $3x^2 \ge 0$ and $k > 0$ , so the sum is positive. True.
A derivative positive everywhere makes $f$ strictly increasing on $\mathbb{R}$ , so A is true and R explains it.

Concept: A constant that keeps a cubic increasing
Typical timeTypical: 90 s
Your timeYours: —

The rule this testsConditions on a constant

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

Assertion (A): f(x)=x3+kxf(x) = x^3 + kxf(x)=x3+kx is strictly increasing on R\mathbb{R}R for every k>0k > 0k>0.Reason (R): When k>0k > 0k>0, f′(x)=3x2+k>0f'(x) = 3x^2 + k > 0f′(x)=3x2+k>0 for every real xxx.

Explanation

Assertion (A): $f(x) = x^3 + kx$ is strictly increasing on $\mathbb{R}$ for every $k > 0$ .
Reason (R): When $k > 0$ , $f'(x) = 3x^2 + k > 0$ for every real $x$ .