Answer :

We are given with a polynomial function f(x) = x^{2} - 4x + 7, and we have to f ‘(x) it’s value at

x = 5 and x = , so by using the formula, f ‘(c) = , we get,

f ‘(5) =

f ‘(5) =

f ‘(5) =

f ‘(5) =

f ‘(5) = lim_{x}_{→}_{5} (x + 1) = 6

Hence to function is differentiable at x = 5 and has value 6 .

f ‘() =

f ‘() =

f ‘() =

f ‘() =

f ‘() =

f ‘() =

f ‘() = = 3

Therefore f ‘(5) = 2f ‘() = 6,

Hence, proved.

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