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\n\n$f(x)=x^{2}-5x + 4$
Answer
Explanation:
Step1: Find f(x + h)
Substitute (x+h) into (f(x)): [ \begin{align*} f(x + h)&=(x + h)^2-5(x + h)+4\ &=x^{2}+2xh+h^{2}-5x-5h + 4 \end{align*} ]
Step2: Calculate f(x + h) - f(x)
[ \begin{align*} f(x + h)-f(x)&=(x^{2}+2xh+h^{2}-5x-5h + 4)-(x^{2}-5x + 4)\ &=x^{2}+2xh+h^{2}-5x-5h + 4-x^{2}+5x - 4\ &=2xh+h^{2}-5h \end{align*} ]
Step3: Find the difference quotient
[ \begin{align*} \frac{f(x + h)-f(x)}{h}&=\frac{2xh+h^{2}-5h}{h}\ &=\frac{h(2x + h-5)}{h}\ &=2x+h - 5 \end{align*} ]
Answer:
(2x+h - 5)