Assertion (A): f(x) = log x is strictly increasing on (0, ∞). Reason (R): d/dx(log x) = 1/x, which is positive for x > 0.

Increasing & Decreasing Functions · Question 14 of 74

Question 14

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Assertion (A): $f(x) = \log x$ is strictly increasing on $(0, \infty)$ .
Reason (R): $\frac{d}{dx}(\log x) = \frac{1}{x}$ , which is positive for $x > 0$ .

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 is true, and a positive derivative on an interval makes the function strictly increasing there.
So A is true and R explains it.

Concept: The derivative test
Typical timeTypical: 60 s
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Assertion (A): f(x)=log⁡xf(x) = \log xf(x)=logx is strictly increasing on (0,∞)(0, \infty)(0,∞).Reason (R): ddx(log⁡x)=1x\frac{d}{dx}(\log x) = \frac{1}{x}dxd​(logx)=x1​, which is positive for x>0x > 0x>0.

Explanation

Assertion (A): $f(x) = \log x$ is strictly increasing on $(0, \infty)$ .
Reason (R): $\frac{d}{dx}(\log x) = \frac{1}{x}$ , which is positive for $x > 0$ .