Consider a strictly decreasing (i.e., implies ) and differentiable function , with derivative . Which of the following may be true about ?
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DSE 2007 Question 13: Limits, continuity and differentiability
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Consider a strictly decreasing (i.e., x>y implies f(x)<f(y)) and differentiable function f:ℜ→ℜ, with derivative Df(x). Which of the following may be true about f? (A) Df(x)>0 for some x∈ℜ (B) Df(x)=0 for some x∈ℜ (C) Df(x)=0 for every x∈(a,b) where a<b (D) Df(x)≥ 0 for every x∈ℜ
Also written as: Consider a strictly decreasing (i.e., x>y implies f(x)<f(y)) and differentiable function f: Re -> Re, with derivative Df(x). Which of the following may be true about f?
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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Question from the DSE 2007 paper. Solutions are TestStop's own. Not affiliated with or endorsed by any examination authority.