Moira uses a difference quotient to determine the average rate of change of f(x) = x2 + 14x from x = –11 to x = 8. She shows the following work.

Determine f(x + h):

f(x + h)

= (x + h)2 + 14(x + h)

= x2 + 2xh + h2 + 14x + 14h

Simplify the difference quotient:

StartFraction f (x + h) minus f (x) Over h EndFraction = StartFraction (x squared + 2 x h + h squared + 14 x + 14 h) minus (X squared + 14 x) Over h EndFraction = StartFRaction x squared + 2 x h + h squared + 14 x + 14 h minus x squared minus 14 x Over h EndFraction = StartFraction 2 x h + h squared + 14 h Over h EndFraction = 2 x + h + 14

Evaluate the difference quotient:

2x + h + 14

= 2(–11) + 8 + 14

= –22 + 8 + 14

= 0

Which statement summarizes Moira’s work?

She correctly found the average rate of change.
She expanded the expression for f(x + h) incorrectly.
She simplified the difference quotient StartFraction f (x + h) minus f (x) Over h EndFraction incorrectly.
She substituted incorrectly when evaluating the difference quotient.