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Questions › DSE › DSE 2013 › Q2
1 markMathematics › Limits, continuity and differentiability › Mean value theorem and Rolle's theoremEasyabout 1 min

DSE 2013 Question 2: Limits, continuity and differentiability

Suppose f:ℜ→ℜf:\Re\to\Ref:ℜ→ℜ. If fff is differentiable, f(3)=2f(3)=2f(3)=2, and 3≤f′(x)≤43\le f'(x)\le 43≤f′(x)≤4 for all xxx, then it must be that f(5)f(5)f(5) lies in the following interval:

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Suppose f:ℜ→ℜ. If f is differentiable, f(3)=2, and 3≤ f′(x)≤ 4 for all x, then it must be that f(5) lies in the following interval: (A) [8,10] (B) [0,8) (C) (10,∞) (D) [3,4]

Also written as: Suppose f: Re -> Re. If f is differentiable, f(3)=2, and 3<= f'(x)<= 4 for all x, then it must be that f(5) lies in the following interval:

Limits, continuity and differentiability has come up 122 times in 7 exams since 2006.

What this question tests

This question is on Mean value theorem and Rolle's theorem, part of Limits, continuity and differentiability in Mathematics.

Results linking the average rate of change to a derivative at some point.

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Question from the DSE 2013 paper. Solutions are TestStop's own. Not affiliated with or endorsed by any examination authority.