find the difference quotient $f(x)$\n$f(x)=3x^{2}+7$\nsimplify your answer as much\n$\\frac{f(x +…

find the difference quotient $f(x)$\n$f(x)=3x^{2}+7$\nsimplify your answer as much\n$\\frac{f(x + h)-f(x)}{h}=\\square$\n

find the difference quotient $f(x)$\n$f(x)=3x^{2}+7$\nsimplify your answer as much\n$\\frac{f(x + h)-f(x)}{h}=\\square$\n

Answer

Explanation:

Step1: Find ( f(x + h) )

Substitute ( x + h ) into ( f(x)=3x^{2}+7 ). [ \begin{align*} f(x + h)&=3(x + h)^{2}+7\ &=3(x^{2}+2xh+h^{2})+7\ &=3x^{2}+6xh + 3h^{2}+7 \end{align*} ]

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

[ \begin{align*} f(x + h)-f(x)&=(3x^{2}+6xh + 3h^{2}+7)-(3x^{2}+7)\ &=3x^{2}+6xh + 3h^{2}+7 - 3x^{2}-7\ &=6xh+3h^{2} \end{align*} ]

Step3: Compute ( \frac{f(x + h)-f(x)}{h} )

[ \begin{align*} \frac{f(x + h)-f(x)}{h}&=\frac{6xh + 3h^{2}}{h}\ &=\frac{h(6x + 3h)}{h}\ &=6x+3h \end{align*} ]

Answer:

(6x + 3h)