If the Mean value theorem is $f(b) - f(a) = (b - a)f^{'}(c)$ Then, for the function $x^{2} - 2x + 3$ in $\left\lbrack 1,\frac{3}{2} \right\rbrack$, the value of $c$ is

Question

Dr. Abubacker · Accepted Answer

(b)
Let $f(x) = x^{2} - 2x + 3$
Since, $f^{'}(c) = \frac{f\left( \frac{3}{2} \right) - f(1)}{\frac{3}{2} - 1}$ [given]
$\Rightarrow \ \ \ \ \ \ 2c - 2 = \frac{\frac{9}{4} - \frac{6}{2} + 3 - (1 - 2 + 3)}{\frac{3}{2} - 1} = \frac{1}{2}$
$\Rightarrow \ \ \ \ \ \ \ c = \frac{5}{4}\  \in \ \left\lbrack 1,\frac{3}{2} \right\rbrack$

Q. If the Mean value theorem is $f(b) - f(a) = (b - a)f^{'}(c)$ Then, for the function $x^{2} - 2x + 3$ in $\left\lbrack 1,\frac{3}{2} \right\rbrack$, the value of $c$ is

Explanation

Reviewed by Dr. Abubacker

Want more practice?