Q. If $(x) = x^{2} - 2x + 4$ on [1, 5], then the value of a constant $c$ such that $\frac{f(5) - f(1)}{5 - 1} = f^{'}(c)$, is
A) 0
B) 1
C) 2
D) 3
Explanation
(b)
Given, $f(x) = x^{2} - 2x + 4$
$f^{'}(x) = 2x - 2$
By applying Mean value theorem
$f^{'}(c) = 2c - 2 = 0$
$\Rightarrow c = 1$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.