Find the number c that satisfies the Mean Value Theorem on the interval (1,4) where f(x)=sqrt(x)
So far I have the f'(c)= (f(4)-f(1))/(4-1) and f'(x)=1/(2sqrt(x)) I'm confused because it's a square root and I'm not sure if my answer for f'(c) is positive or negative. If I go with positive the value c is not in my interval. Please help! Thanks!

Question

Find the number c that satisfies the Mean Value Theorem on the interval (1,4) where f(x)=sqrt(x)
So far I have the f'(c)= (f(4)-f(1))/(4-1) and f'(x)=1/(2sqrt(x)) I'm confused because it's a square root and I'm not sure if my answer for f'(c) is positive or negative. If I go with positive the value c is not in my interval. Please help! Thanks!

myininaya · Answer

so good so far
so you have 1/(2sqrt(c))=(2-1)/(4-1) right?

myininaya · Answer

you should get one answer

myininaya · Answer

i would start off by taking the reciprocal of both sides

myininaya · Answer

let me know if you have problems after that

anonymous · Answer

Oh the reciprocal! Gosh, I completely forgot haha. Ok, so I think I end up with x=9/4 which is 2.25 and that is in my interval! Woohoo Thank you SO much!

myininaya · Answer

np