Question

Let $f\left(x\right)=\sqrt{5x-1}$ and let $c$ be the number that satisfies the Mean value theorem for $f$ on the interval $[1,10]$.

Find the value of $c$.

• A. $2.25$
• B. $3.25$
• C. $4.25$
• D. None of the above

Answer 1

The correct option is C $4.25$

Given, $f\left(x\right)=\sqrt{5x-1}$

From mean value theorem we have $f^{\prime }\left(c\right)=\frac{f\left(b\right)-f\left(a\right)}{b-a}$

$\frac{5}{2\sqrt{5x-1}}=\frac{7-2}{9}=\frac{5}{9}$

$\Rightarrow c=\frac{17}{4}=4.25$

Mean value theorem states that for a continuous function $f\to (a,b)$ and differential on $(a,b)c\in (a,b)$ such that $f^{\prime }\left(c\right)=\frac{f\left(b\right)-f\left(a\right)}{b-a}$