Question

for the function $f(x)=3x - 6$, evaluate and simplify.
$\frac{f(x + h)-f(x)}{h}$
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for the function $f(x)=2x^{2}-2x$, evaluate and simplify.
$\frac{f(x + h)-f(x)}{h}$
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for the function $f(x)=4x^{2}+5x$, evaluate and simplify.
$\frac{f(x + h)-f(x)}{h}$
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Explanation:

Question 16

Step1: Find \(f(x + h)\)

Given \(f(x)=3x - 6\), then \(f(x + h)=3(x + h)-6=3x+3h - 6\)

Step2: Substitute into \(\frac{f(x + h)-f(x)}{h}\)

$$
LATEXBLOCK0
$$

Question 17

Step1: Find \(f(x + h)\)

Given \(f(x)=2x^{2}-2x\), then \(f(x + h)=2(x + h)^{2}-2(x + h)\)

$$
LATEXBLOCK1
$$

Step2: Substitute into \(\frac{f(x + h)-f(x)}{h}\)

$$
LATEXBLOCK2
$$

Question 18

Step1: Find \(f(x + h)\)

Given \(f(x)=4x^{2}+5x\), then \(f(x + h)=4(x + h)^{2}+5(x + h)\)

$$
LATEXBLOCK3
$$

Step2: Substitute into \(\frac{f(x + h)-f(x)}{h}\)

$$
LATEXBLOCK4
$$

Answer:

1. $3$
2. $4x + 2h - 2$
3. $8x + 4h + 5$