Answer:
2.25
Explanation:
The computation of the number c that satisfied is shown below:
Given that

Interval = (0,9)
According to the Rolle's mean value theorem,
If f(x) is continuous in {a,b) and it is distinct also
And, f(a) ≠ f(b) so its existance should be at least one value
i.e

After this,


After this,
Put the values of a and b to the above equation
![f^i(c) = (f(b) - f(a))/(b - a) \\\\ \frac{1}{{2}√(c) } = (3 -0)/(9-0) \\\\ \frac{1}{\sqrt[2]{c} } = (3)/(9) \\\\ \frac{1}{\sqrt[2]{c} } = (1)/(3) \\\\ \sqrt[2]{c} = 3\\\\√(c) = (3)/(2) \\\\ c = (9)/(4)](https://img.qammunity.org/2021/formulas/mathematics/college/6ph3c98vl8r8ayz8oscai1zlyupxgg9z7y.png)
= 2.25