Definite Integration Question 44

Question 44

  1. If f′′(x)<0,∀x∈(a,b), and (c,f(c)) is point of maxima, where c∈(a,b), then f′(c) is (a) f(b)−f(a)b−a (b) 3f(b)−f(a)b−a (c) 2f(b)−f(a)b−a (d) 0
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Solution:

  1. F′(c)=(b−a)f′(c)+f(a)−f(b)

F′′(c)=f′′(c)(b−a)<0 ⇒F′(c)=0⇒f′(c)=f(b)−f(a)b−a

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