Question

1. (0 points) calculate the difference quotient (dq) of the given function. simplify your answer fully.

(a) (f(x) = x^3).

(dq =)

Explanation:

Step1: State the formula

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

Step2: Substitute the function

$$DQ = \frac{(x+h)^3 - x^3}{h}$$

Step3: Expand the numerator

$$DQ = \frac{x^3 + 3x^2h + 3xh^2 + h^3 - x^3}{h}$$

Step4: Simplify the numerator

$$DQ = \frac{3x^2h + 3xh^2 + h^3}{h}$$

Step5: Divide by h

$$DQ = 3x^2 + 3xh + h^2$$

Answer:

\(DQ = 3x^2 + 3xh + h^2\)