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  4. If f(x) = x2 - 2x + 4 on [1, 5], then the value of a constant c such that (f(5) - f(1)/5 - 1) = f'(c), is:

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Q. If $f(x) = x^2 - 2x + 4$ on [1, 5], then the value of a constant c such that $\frac{f(5) - f(1)}{5 - 1} = f'(c)$, is:

Application of Derivatives

Solution:

Given $f (x) = x^2 - 2x + 4$
$\therefore \, f'(x) = 2x - 2$
So, $f'(c) = 2c - 2$
So, $2c - 2 = \frac{f(5) - f(1)}{5 - 1}$
$\Rightarrow \, f(5) = (5)^2 - 2 (5) + 4 = 19$ and $f(1) = (1)^2 - 2(1) + 4 = 3$
$\Rightarrow \, 2c - 2 = \frac{19 - 3}{4} = 4 \, \Rightarrow \, 2c - 6$
Thus $c = 3.$