Difference Quotient.

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Presentation transcript:

Difference Quotient

Consider the function y=3x What is its slope? Does the slope ever change?

Consider the function y=5 𝑥 2 What is its slope? Does the slope ever change?

The Difference Quotient The difference quotient finds the rate of change for a function in a small neighborhood. It’s defined as 𝑓 𝑥+ℎ −𝑓(𝑥) ℎ , or sometimes as 𝑓 𝑥+𝛥𝑥 −𝑓(𝑥) 𝛥𝑥

Calculate the difference quotient for the following function 𝑓 𝑥 =10𝑥+2

Calculate the difference quotient for the following function 𝑓 𝑥 = 𝑥 2

Calculate the difference quotient for the following function 𝑓 𝑥 = 𝑒 𝑥

Instantaneous rate of change lim ℎ→0 𝑓 𝑥+ℎ −𝑓(𝑥) ℎ

Find the instantaneous rate of change for the following functions 𝑓 𝑥 = 𝑥 2 𝑔 𝑥 = 𝑥 3 ℎ 𝑥 = 1 𝑥 𝑓 𝑥 = 𝑒 𝑥