Question

find and simplify the difference quotient $\frac{f(x + h)-f(x)}{h}$, $h
eq0$ for the given function. $f(x)=3x^{2}$ $\frac{f(x + h)-f(x)}{h}=square$ (simplify your answer.)

Explanation:

Step1: Find f(x + h)

Substitute \(x+h\) into \(f(x)=3x^{2}\), so \(f(x + h)=3(x + h)^{2}=3(x^{2}+2xh+h^{2})=3x^{2}+6xh + 3h^{2}\)

Step2: Calculate f(x + h)-f(x)

\(f(x + h)-f(x)=(3x^{2}+6xh + 3h^{2})-3x^{2}=6xh+3h^{2}\)

Step3: Calculate the difference - quotient

\(\frac{f(x + h)-f(x)}{h}=\frac{6xh + 3h^{2}}{h}=\frac{h(6x + 3h)}{h}=6x+3h\)

Answer:

\(6x + 3h\)