Q4 Verify Mean Value Theorem, if in the interval [a, b], where
a = 1 and b = 4.
Condition for M.V.T.
a ) f is continuous in [a,b]
b ) f is differentiable in (a,b)
Then, there exist a c in (a,b) such that
It is given that
and interval is [1,4]
Now, f is a polynomial function , is continuous in[1,4] and differentiable in (1,4)
Then, by Mean value theorem we can say that their exist a c in (1,4) such that
Hence, mean value theorem is verified for the function