Unit V Big Question

Difference Quotient

1. Explain in detail where the formula for the difference quotient comes from. Include all appropriate terminology.

f(x+h)-f(x)/h 

This formula is derived to find the slope, or derivative, of a tangent, or secant line, that touches a point on an original graph. A tangent lint will touch at a point once, while a secant line will touch twice. When we use the difference quotient to find the derivative of the slope, we plug in the point it crosses into "h". We do this using limit notation, which is the limit as h approaches a number is f(x).