Posted by **Sasha** on Sunday, November 7, 2010 at 8:17pm.

verify that the function satisfies the hypothesis of the mean value theorem on the given interval. then find all numbers c that satisfy the conclusion of the mean value theorem.

f(x) = x/(x+2) , [1,4]

- calculus -
**dow**, Sunday, November 7, 2010 at 9:48pm
f(b)-f(a)/b-a = f'(c) MVT

to find f(b) and f(a), just plug endpoints into original function

f(b) = f(4) = (2/3)

f(a) = f(1) = (1/3)

(2/3)-(1/3)

----------- = f'(c)

4 - 1

(1/9) = f'(c)

next, find derivative of f(x)

f'(c) = f'(x)

product rule

(1/9) = (x)(x+2)^-1

(1/9) = (x+2)^-1 - x(x+2)^-2

(1/9) = (1/x+2) - (x/(x+2))^2

(1/9) = (1/x+2) * (1 - (x/(x+2))

(1/x+2) = (1/9) mult. ea s. by 9

(9/x+2) = 1

9 = x + 2

7 = x

I'm sure you can solve the other x

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