Question

(b) (f(x) = 5x^2 - 8).

(dq = )

Explanation:

Step1: State the difference quotient formula

$$DQ = \frac{f(x+h) - f(x)}{h}$$

Step2: Substitute the function into the formula

$$DQ = \frac{[5(x+h)^2 - 8] - [5x^2 - 8]}{h}$$

Step3: Expand the numerator

$$DQ = \frac{5(x^2 + 2xh + h^2) - 8 - 5x^2 + 8}{h}$$

Step4: Simplify the numerator

$$DQ = \frac{5x^2 + 10xh + 5h^2 - 5x^2}{h}$$

Step5: Combine like terms

$$DQ = \frac{10xh + 5h^2}{h}$$

Step6: Divide by h

$$DQ = 10x + 5h$$

Answer:

\(10x + 5h\)