Q5 Verify Mean Value Theorem, ifin the interval [a, b], where
a = 1 and b = 3. Find all for which f '(c) = 0.
Condition for M.V.T.
a ) f is continuous in [a,b]
b ) f is differentiable in (a,b)
Then, their exist a c in (a,b) such that
It is given that
and interval is [1,3]
Now, f being a polynomial function , is continuous in[1,3] and differentiable in (1,3)
Then, by Mean value theorem we can say that their exist a c in (1,4) such that
Hence, mean value theorem is varified for following function and is the only point where f '(c) = 0