Determine the difference quotient:

Question

Examine the function below: f(x)=x²-3

 

Determine the difference quotient:( f(x+h)-f(x) )/h

 

Enter final results

Answer 1

f(x) = x² - 3

 

f(x + h) - f(x) = [(x + h)² - 3] - (x² - 3) = (x² +2xh + h² - 3)  - (x² - 3)

 

f(x + h) - f(x) = 2xh + h² 

 

[f(x + h) - f(x)] / h = (2xh + h²) / h = 2x + h