If f (x) = 4x² + 3x - 5, then f(x+h)-f(x)/ h is equal to which of the following?

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asked May 23, 2023 232k views

2 votes

If f (x) = 4x² + 3x - 5, then f(x+h)-f(x)/ h is equal to which of the following?

Mathematics
high-school

Danja asked

by Danja

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1 Answer

3 votes

Answer:

8x + 4h + 3

Explanation:

$f(x)=4x^2 + 3x-5 \\ \\ f(x+h)=4(x+h)^2+3(x+h)-5 \\ \\ =4(x^2+2xh+h^2)+3x+3h+5 \\ \\ =4x^2+8xh+4h^2+3x+3h+5 \\ \\ f(x+h)-f(x)=(4x^2+8xh+4h^2+3x+3h+5)-(4x^2+3x+5) \\ \\ =8xh+4h^2+3h \\ \\ (f(x+h)-f(x))/(h)=(8xh+4h^2+3h)/(h)=8x+4h+3$

MichalMoskala answered May 29, 2023

by MichalMoskala

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