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Questions › DSE › DSE 2012 › Q47
2 marksMathematics › Concavity, convexity and quasi-concavity › Testing concavity and convexityHardabout 3 min

DSE 2012 Question 47: Concavity, convexity and quasi-concavity

Suppose that f(x)f(x)f(x) is twice differentiable and strictly concave in xxx. Define, g(x)=lim⁡t→xf(c+t)−f(c+x)t−xg(x)=\lim_{t\to x}\dfrac{f(c+t)-f(c+x)}{t-x}g(x)=limt→x​t−xf(c+t)−f(c+x)​ where ccc is a constant. Then g(x)g(x)g(x) is

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Suppose that f(x) is twice differentiable and strictly concave in x. Define, g(x)=lim_(t→ x)(f(c+t)-f(c+x))/(t-x) where c is a constant. Then g(x) is (A) Decreasing function (B) Increasing function (C) Decreasing function when c > 0 and increasing function when c < 0 (D) Increasing function when c > 0 and decreasing function when c < 0

Also written as: Suppose that f(x) is twice differentiable and strictly concave in x. Define, g(x)=lim_(t-> x)(f(c+t)-f(c+x))/(t-x) where c is a constant. Then g(x) 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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Practise Concavity, convexity and quasi-concavityMore on Testing concavity and convexity

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