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The number of continous and derivable fu...

The number of continous and derivable function(s) f(x) such that f(1) = -1 , f(4) = 7 and `f'(x) gt 3` for all x `in` R is are :

A

0

B

1

C

3

D

infinite

Text Solution

Verified by Experts

The correct Answer is:
A
Using LMVT in [1, 4] for y = f(x)
there must exist atleast one c `in` (1, 4) such that
f'("c") = (f(4) - f(1))/(4 - 1) = (8)/(3) but `f'(x) > 3 AA x in R`
Hence , no such function exists.
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