1)

The value of x in the interval [4,9] at which the function f(x) = √x satisfies the mean value theorem is

A) 13/4

B) 17/4

C) 21/4

D) 25/4

Option D

### Explanation:

(i) f(x) = √x is continuous in[4,9]

(ii) $f'(x) = \frac{1}{2\sqrt{x}}$

Thus f(x) is differentiable in (4, 9) (iii) f(4) ≠ f(9)

All the three conditions of LMV theorem satisfied then there exist at least one c Ε (4,9) such that.

f'(c) = $\frac{f(b)-f(a)}{b-a}$ = $\frac{1}{2\sqrt{c}}$ = 1/5

c = 25/4