MEan value Theorem help!?

Question

Verify that the hypotheses of the Mean Value Theorem are satisfied for each of the functions on the given
interval, and find the value of "c" which Mean Value Theorem guarantees.

f(x)= 4 − √x on [1, 9]

Answer 1

f(x) is continuous on [1, 9] and is differentiable on (1, 9).  So, the Mean Value Theorem does apply.  

 

According to the theorem, there is at least one number, c, where       1 < c < 9 and such that f'(c) = [f(9) - f(1)]/(9 - 1).

 

So, -1/(2√c) = (1 - 3)/8

 

-1/(2√c) = -1/4      Therefore, 2√c = 4

 

                                                          √c = 2

 

                                                            c = 4