find the difference quotient of f(x)=x² - 8; that is find (f(x + h)-f(x))/h, h≠0. be sure to simplify. the…
find the difference quotient of f(x)=x² - 8; that is find (f(x + h)-f(x))/h, h≠0. be sure to simplify. the difference quotient is
Answer
Explanation:
Step1: Find f(x + h)
Given (f(x)=x^{2}-8), then (f(x + h)=(x + h)^{2}-8=x^{2}+2xh+h^{2}-8)
Step2: Substitute f(x + h) and f(x) into the difference - quotient formula
(\frac{f(x + h)-f(x)}{h}=\frac{(x^{2}+2xh + h^{2}-8)-(x^{2}-8)}{h})
Step3: Simplify the numerator
((x^{2}+2xh + h^{2}-8)-(x^{2}-8)=x^{2}+2xh + h^{2}-8 - x^{2}+8=2xh+h^{2}) So, (\frac{f(x + h)-f(x)}{h}=\frac{2xh + h^{2}}{h})
Step4: Factor out h from the numerator and simplify
(\frac{2xh + h^{2}}{h}=\frac{h(2x + h)}{h}=2x + h)
Answer:
(2x + h)