Questions
f (x) is continuous on [0, 2] , differentiable on (0,2) , f(0) = 2 , f(2) = 8 and for all x in (0,2) , then the value of f(1)
a
2
b
3
c
4
d
5
detailed solution
Correct option is D
f(0)=2 f(2)=8f′(x)≤3C1∈(0,1),f′(x)=f(1)−f(0)1−0f′C1≤3⇒f(1)−21≤3f(1)≤5C2∈(1,2),f′(x)=f(2)−f(1)2−1≤38−f(1)1≤3f(1)≥5⇒f(1)=5Talk to our academic expert!
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