Question

Consider the function $f\left(x\right)=8x^2-7x+5$ on the interval $[-6,6].$ The value of $c$ that satisifies the conclusion of the mean value theorem is

• A. $-\frac{7}{8}$
• B. $-4$
• C. $\frac{7}{8}$
• D. $0$

Answer 1

The correct option is D $0$

The given function is continuous on $[-6,6]$ and differentiable on $(-6,6)$.

Hence application LMVT gives us

$\frac{f\left(6\right)-f(-6)}{6-(-6)}=f^{\prime }\left(c\right)$

$\frac{251-335}{12}=16c-7$

$16c-7=\frac{-84}{12}$

$16c-7=-7$
$c=0$.