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Questions › DSE › DSE 2011 › Q24
2 marksMathematics › Concavity, convexity and quasi-concavity › Testing concavity and convexityModerateabout 3 min

DSE 2011 Question 24: Concavity, convexity and quasi-concavity

Let fff be a real valued differentiable function defined for all x≥ax\ge ax≥a. Consider the function FFF defined by F(x)=∫axf(t) dtF(x)=\int_{a}^{x}f(t)\,dtF(x)=∫ax​f(t)dt. If fff is increasing on any interval, then on that interval FFF is

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Let f be a real valued differentiable function defined for all x≥ a. Consider the function F defined by F(x)=∫ₐ^xf(t) dt. If f is increasing on any interval, then on that interval F is (A) convex (B) concave (C) increasing (D) decreasing

Also written as: Let f be a real valued differentiable function defined for all x>= a. Consider the function F defined by F(x)= integral_a^xf(t) dt. If f is increasing on any interval, then on that interval F is

Concavity, convexity and quasi-concavity has come up 39 times in 6 exams since 2006.

What this question tests

This question is on Testing concavity and convexity, part of Concavity, convexity and quasi-concavity in Mathematics.

Checking concavity or convexity from a definition, derivatives or operations that preserve it.

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Question from the DSE 2011 paper. Solutions are TestStop's own. Not affiliated with or endorsed by any examination authority.