Question

Find the number c that satisfies the conclusion of the Mean Value Theorem.
f(x)= x/x+2
[1,4]

Answer 1

Okay, so the MVT states that at some point c in this interval, f'(c) = [f(b) - f(a)]/(b-a).
Set a = 1 and b = 4. You get f(a) = f(1) = (1/3)
f(b) = f(4) = (2/3)
Plugging these in, you would get f'(c) = (1/9).
f'(c) would equal 2/(c+2)^2.
Then solve the quadratic equation.

Answer 2

Anyone confirm?

Answer 3

how would i solve it?

Answer 4

Use the quadratic formula and the answer should be about 2.243.

Answer 5

oh, thank you!!!!!!!!!

Answer 6

\[\frac{1}{9}=\frac{2}{(c+2)^2}\]

\[9=\frac{(c+2)^2}{2}\]

\[\sqrt{9\cdot2}=c+2\]

\[c=3\sqrt{2}-2\]

Answer 7

thanks!