Question

find and simplify the difference quotient $\frac{f(x + h)-f(x)}{h}$, $h
eq0$ for the given function.
$f(x)=6x^{2}$
$\frac{f(x + h)-f(x)}{h}=square$ (simplify your answer.)

Explanation:

Step1: Find f(x + h)

Substitute \(x+h\) into \(f(x)=6x^{2}\), so \(f(x + h)=6(x + h)^{2}=6(x^{2}+2xh+h^{2})=6x^{2}+12xh + 6h^{2}\)

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

\(f(x + h)-f(x)=(6x^{2}+12xh + 6h^{2})-6x^{2}=12xh+6h^{2}\)

Step3: Calculate the difference - quotient

\(\frac{f(x + h)-f(x)}{h}=\frac{12xh + 6h^{2}}{h}=\frac{h(12x + 6h)}{h}=12x+6h\)

Answer:

\(12x + 6h\)