find the difference quotient of f(x)=x² - 3; that is find (f(x + h)-f(x))/h, h≠0. be sure to simplify. the…
find the difference quotient of f(x)=x² - 3; 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)
$f(x+h)=(x + h)^2-3=x^{2}+2xh+h^{2}-3$
Step2: Substitute f(x + h) and f(x) into the difference - quotient formula
$\frac{f(x + h)-f(x)}{h}=\frac{(x^{2}+2xh+h^{2}-3)-(x^{2}-3)}{h}$
Step3: Simplify the numerator
$\frac{x^{2}+2xh+h^{2}-3 - x^{2}+3}{h}=\frac{2xh+h^{2}}{h}$
Step4: Factor out h from the numerator and cancel out h
$\frac{h(2x + h)}{h}=2x+h$
Answer:
$2x + h$