# Average rate of change

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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.

• Average rate of change -

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 = (0-2)/(-1+3) = -1
if g=-4
g(-4) = 6, and avag rate = (6-2)/(-4+3) = -4 ≠ -1

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