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How do you find and simplify f(x + h) − f(x) and

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14x + h

14x + 14h

x + h

h+ 14x
𝑓(𝑥 + ℎ) − 𝑓(𝑥), given f(x) = 7𝑥2 − 1 ?ℎ

answer is B.

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Detailed Solution

f(x) = 7𝑥2 − 1
f(x + h) = 7(𝑥 + ℎ)2 − 1
f(x + h) = 7𝑥2 + 14𝑥ℎ + 14ℎ2 − 1
f(x + h) − f(x) = 7𝑥2 + 14𝑥ℎ + 14ℎ2 − 1 − 7𝑥2 + 1
= 14𝑥ℎ + 14ℎ2
𝑓(𝑥 + ℎ) − 𝑓(𝑥)
=
ℎ

14𝑥ℎ + 14ℎ2

ℎ
𝑓(𝑥 + ℎ) − 𝑓(𝑥)

ℎ

= 14𝑥ℎ + 14ℎ

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