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Mathematics, 21.05.2021 18:30 s108870
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.
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Moira uses a difference quotient to determine the average rate of change of f(x) = x2 + 14x from x =...
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