math  very urgent !
posted by Carla on .
Verify that f(x) = x^3 − 2x + 6 satisfies the hypothesis of the MeanValue Theorem over the interval [2, 3]
and find all values of C that satisfy the conclusion of the theorem.

f' = 3 x^2 2
at 2 f(2) = 8+4+6 = 2
at 3 f(3) = 276+6 = 27
mean slope = (272)/5 = 5
is f' = 5 in between 2 and +3?
5 = 3 x^22
3 x^2 = 7
x^2 = 7/3
x =  1.53 and +1.53
both are between x = 2 and x = +3