Question

The point where the function $f\left(x\right)=x^2-5x-6$ satisfies the condition of Rolle’s theorem is

• A. $x=5$
• B. $x=\frac{5}{2}$
• C. $x=6$
• D. None of these

Answer 1

The correct option is B

$x=\frac{5}{2}$

Explanation for the correct option:

Find the point satisfying Rolle's theorem

In the question, a function $f\left(x\right)=x^2-5x-6$ is given.

Since the given function is a polynomial, so, the given function is continuous and differentiable all over the domain.

According to Rolle's theorem, if a function is continuous all over the domain then there exists at least one value for which $f\text{'}\left(x\right)=0$.

Find the derivative of the given function.

$f\text{'}\left(x\right)=2x-5$.

Now, put the derivative of the given function equal to zero to find the required point.

$$\begin{gathered} 2x-5=0 \\ \Rightarrow x=\frac{5}{2} \end{gathered}$$.

Therefore, at $x=\frac{5}{2}$ the function $f\left(x\right)=x^2-5x-6$ satisfies the condition of Rolle’s theorem.

Hence, option $B$ , $x=\frac{5}{2}$ is the correct answer.