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?

Question

clara1223 · Answer

@zepdrix can you help me?

loser66 · Answer

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?

clara1223 · Answer

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!

loser66 · Answer

np