SOLUTION: y = √x, [16, 25] Calc I its asking to find c usting MVT
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Question 230599: y = √x, [16, 25] Calc I its asking to find c usting MVT
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
That is a pretty cryptic question you have posed there. I'm guessing that you want to find a critical point of the function 
on the closed interval [16, 25] using the Mean Value Theorem.
The Mean Value Theorem says:
Let 
[a, b]
be a continuous function on the closed interval [a, b] and differentiable on the open interval (a, b), where 
. Then there exists some 
in (a, b) such that:
\ =\ \frac{f(b)-f(a)}{b-a})
The given interval is [16, 25] and \ =\ \sqrt{x})
, so:
-f(a)}{b-a}\ =\ \frac{5-4}{25-16}\ =\ \frac{1}{9})
But given
\ =\ -\frac{1}{2\sqrt{x}}\ \ \ \ )
(using the power rule with \ =\ x^{\frac{1}{2}})
)
Therefore, if
\ =\ \frac{1}{9})
then
Solve for 
John
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