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If f (x) is continous on [0,2], differen...

If f (x) is continous on [0,2], differentiable in `(0,2) f (0) =2, f(2)=8 and f '(x) le 3 ` for all x in (0,2), then find the value of f (1).

A

4

B

5

C

6

D

7

Text Solution

Verified by Experts

The correct Answer is:
B
Applying LMVT to f in `[0,1]` and again in `[1,2]` there exist `C_(1)in (0,1)` such that
`(f(1)-f (0))/(1-0) =f'C_(1)1 le 3 impliesf(1) le 5 " "...(i)`
There exist `C _(2) in (1,2),` such that
`(f(2)-f (1))/(2-1) =f'(C_(2))le 3 implies f (1) ge 5`
Hence, (1) and (2) imply that `f (1) =5`
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