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Q.

f (x) is continuous on [0, 2] , differentiable on (0,2) , f(0) = 2 , f(2) = 8  and  f'(x) ≤ 3 for all x in (0,2) , then  the value of f(1)

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a

2

b

3

c

4

d

5

answer is D.

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Detailed Solution

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)=5
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