Question

Using the Mean Value Theorem find all numbers c on the interval [0,5] that satisfy the theorem for f(x)=3*sqrt(25-x^2). I have already found that (f(5)-f(0))/(5-0)=-3, and that the derivative of the function is (-3x)/sqrt(25-x^2). When I set that equal to -3 and solve for x I get an answer that is not in the interval so I am doing something wrong. Can someone help me?

Answer 1

@zepdrix can you help me?

Answer 2

I don't get why you said so,
\(\dfrac{-3x}{\sqrt{25-x^2}}=-3\\x = \sqrt{25-x^2}\)

\(x^2 = 25 -x^2\\2x^2 = 25\\x=\pm\dfrac{5}{\sqrt2}\)
has positive one is on the interval. Am I missing something?

Answer 3

Oh I didnt cancel out the -3 in the beginning and somehow I got my math wrong. I got \[\pm \frac{ 5\sqrt{3} }{ \sqrt{2} }\] Thanks!

Answer 4

np