follow the step by step process to determine the difference quotient, $\frac{f(x + h)-f(x)}{h}$\nf(x)=4x^{2}…

follow the step by step process to determine the difference quotient, $\frac{f(x + h)-f(x)}{h}$\nf(x)=4x^{2}-3\na. determine f(x + h)\nf(x + h)= \n(simplify your answer.)\nb. simplify the expression f(x + h)-f(x)\nf(x + h)-f(x)= \n(simplify your answer. do not factor.)\nc. determine the difference quotient $\frac{f(x + h)-f(x)}{h}$\n$\frac{f(x + h)-f(x)}{h}=$ \n(simplify your answer. do not factor.)

follow the step by step process to determine the difference quotient, $\frac{f(x + h)-f(x)}{h}$\nf(x)=4x^{2}-3\na. determine f(x + h)\nf(x + h)= \n(simplify your answer.)\nb. simplify the expression f(x + h)-f(x)\nf(x + h)-f(x)= \n(simplify your answer. do not factor.)\nc. determine the difference quotient $\frac{f(x + h)-f(x)}{h}$\n$\frac{f(x + h)-f(x)}{h}=$ \n(simplify your answer. do not factor.)

Answer

Explanation:

Step1: Find f(x + h)

Substitute (x+h) into (f(x)): [ \begin{align*} f(x + h)&=4(x + h)^{2}-3\ &=4(x^{2}+2xh+h^{2})-3\ &=4x^{2}+8xh + 4h^{2}-3 \end{align*} ]

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

[ \begin{align*} f(x + h)-f(x)&=(4x^{2}+8xh + 4h^{2}-3)-(4x^{2}-3)\ &=4x^{2}+8xh + 4h^{2}-3 - 4x^{2}+3\ &=8xh+4h^{2} \end{align*} ]

Step3: Determine the difference quotient (\frac{f(x + h)-f(x)}{h})

[ \begin{align*} \frac{f(x + h)-f(x)}{h}&=\frac{8xh + 4h^{2}}{h}\ &=\frac{h(8x + 4h)}{h}\ &=8x+4h \end{align*} ]

Answer:

a. (4x^{2}+8xh + 4h^{2}-3) b. (8xh+4h^{2}) c. (8x + 4h)