find and simplify the difference quotient $\frac{f(x + h)-f(x)}{h}$, $h\neq0$ for the given…

find and simplify the difference quotient $\frac{f(x + h)-f(x)}{h}$, $h\neq0$ for the given function.\n$f(x)=6x^{2}$\n$\frac{f(x + h)-f(x)}{h}=square$ (simplify your answer.)

find and simplify the difference quotient $\frac{f(x + h)-f(x)}{h}$, $h\neq0$ for the given function.\n$f(x)=6x^{2}$\n$\frac{f(x + h)-f(x)}{h}=square$ (simplify your answer.)

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)