Consider a function , where denotes the set of real numbers. If is strictly increasing (i.e., implies ) and differentiable, then the derivative of
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2 marksMathematicsLimits, continuity and differentiabilityIntermediate value theorem, monotonicity and rootsModerateabout 2 min
DSE 2006 Question 52: Limits, continuity and differentiability
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Consider a function f:ℜ→ℜ, where ℜ denotes the set of real numbers. If f is strictly increasing (i.e., x>y implies f(x)>f(y)) and differentiable, then the derivative of f (A) may be less than 0 at some x∈ℜ (B) may be infinite at some x∈ℜ (C) is greater than or equal to 0 at every x∈ℜ (D) is greater than 0 at every x∈ℜ
Also written as: Consider a function f: Re -> Re, where Re denotes the set of real numbers. If f is strictly increasing (i.e., x>y implies f(x)>f(y)) and differentiable, then the derivative of 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 2006 paper. Solutions are TestStop's own. Not affiliated with or endorsed by any examination authority.