# Q5  Verify Mean Value Theorem, if in the interval [a, b], where        a = 1 and b = 3. Find all for which f '(c) = 0.

Condition for M.V.T.
If 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)
And and Then, by Mean value theorem we can say that their exist a c  in (1,4) such that  Now, And Hence, mean value theorem is varified for following function and is the only point where f '(c) = 0

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