Average rate of change
posted by Kjd .
Please help..
Determine the value of "g" so that the average rate of change of the function h(x)=x^2+3x+2 on the interval 3≤x≤g is 1. Thank you.

h(3) = 9  9 + 2 = 2
h(g) = g^2 + 3g + 2
average rate of change = (g^2 + 3g + 2 = 2)/(g+3)
= (g^2 + 3g)/(g+3)
= 1
g^2 + 3g = g  3
g^2 + 4g + 3 = 0
(g+1)(g+4) = 0
g= 1 or g = 4
but 3≤x≤4 is not a valid interval
so g = 1
checking:
if g = 1
f(1) = 0 and avg rate = (02)/(1+3) = 1
if g=4
g(4) = 6, and avag rate = (62)/(4+3) = 4 ≠ 1