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Questions › JNU › JNU SSS 2015 › Q44
2 marks, −0.5Mathematics › Limits, continuity and differentiability › Intermediate value theorem, monotonicity and rootsHardabout 4 min

JNU SSS 2015 Question 44: Limits, continuity and differentiability

Let f(x)f(x)f(x) be a differentiable function defined over the interval [0,2][0, 2][0,2]. It is given that f(0)=1f(0) = 1f(0)=1 and f(x)≤0→f′(x)>0f(x) \leq 0 \rightarrow f'(x) > 0f(x)≤0→f′(x)>0. Then

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Let f(x) be a differentiable function defined over the interval [0, 2]. It is given that f(0) = 1 and f(x) ≤ 0 → f′(x) > 0. Then (A) f(x) < 0 for some x in the interval (0, 2] (B) f(x) ≥ 0 for all x in the interval [0, 2] (C) f(x) = 0 for all x in the interval [0, 1] (D) f(x) is strictly positive for all 0 < x < 1 and f(x) is strictly negative for all 1 < x < 2

Also written as: Let f(x) be a differentiable function defined over the interval [0, 2]. It is given that f(0) = 1 and f(x) <= 0 -> f'(x) > 0. Then

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

What this question tests

This question is on Intermediate value theorem, monotonicity and roots, part of Limits, continuity and differentiability in Mathematics.

Using continuity and the sign of the derivative to show roots exist or are unique.

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Practise Limits, continuity and differentiabilityMore on Intermediate value theorem, monotonicity and roots

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Question from the JNU SSS 2015 paper. Solutions are TestStop's own. Not affiliated with or endorsed by any examination authority.