the difference of quotient of g(x)

Question

G(x)=2x^2+5

What is the difference of quotient of g(x)=

 

Answer 1

g(x)=2x²+5

 

The difference quotient is the slope of the secant line connecting two points, (x,g(x)) and (x+h,g(x+h)), along the curve g(x):

 

[g(x+h)-g(x)]/h

 

= [2(x+h)² + 5 - (2x²+5)]/h

 

= [2x² + 4xh + 2h² + 5 - 2x² - 5]/h

 

= [4xh + 2h²]/h

 

= 4x + 2h