Suppose is decreasing and differentiable, and satisfies . Then is
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2 marks, −0.666666666666667MathematicsConcavity, convexity and quasi-concavityTesting concavity and convexityModerateabout 3 min
DSE 2017 Question 27: Concavity, convexity and quasi-concavity
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Suppose f:ℝ₊→ℝ is decreasing and differentiable, and F:ℝ₊→ℝ satisfies F(x)=∫₀^x f(t) dt. Then F is (A) convex (B) concave (C) increasing (D) decreasing
Also written as: Suppose f:R_+->R is decreasing and differentiable, and F:R_+->R satisfies F(x)= integral_0^x f(t) dt. Then 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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