find the difference quotient of f, that is, find $\frac{f(x + h)-f(x)}{h}$, h $\neq$ 0, for the following…

find the difference quotient of f, that is, find $\frac{f(x + h)-f(x)}{h}$, h $\neq$ 0, for the following function. be sure to simplify. f(x) = $x^{2}-8x + 3$ $\frac{f(x + h)-f(x)}{h}=square$ (simplify your answer.)

find the difference quotient of f, that is, find $\frac{f(x + h)-f(x)}{h}$, h $\neq$ 0, for the following function. be sure to simplify. f(x) = $x^{2}-8x + 3$ $\frac{f(x + h)-f(x)}{h}=square$ (simplify your answer.)

Answer

Explanation:

Step1: Find f(x + h)

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

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

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

Step3: Find the difference quotient

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

Answer:

(2x+h - 8)