Warm Up a) What is the average rate of change from x = -2 to x = 2? b) What is the average rate of change over the interval [1, 4]? c) Approximate y’(2).

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Presentation transcript:

Warm Up a) What is the average rate of change from x = -2 to x = 2? b) What is the average rate of change over the interval [1, 4]? c) Approximate y’(2).

Slope, Tangent & Normal Lines

What is a tangent line? What is a secant line? How do they relate to the graphs of functions?

How do you find the slope of a secant line? What is another name for that slope?

Other names for the slope of the tangent line are “instantaneous rate of change” or “derivative”. Notation for the derivative includes… How do you find the slope of a tangent line? Difference quotient

Use the limit process to find the derivative What does the derivative tell you?

Use the limit process to find the derivative Why does the derivative have an x in the answer? Find the slope of the tangent line at x = 1. (Use the derivative feature of your calculator to check your answer.) Write an equation of the tangent line at x = 1

A normal line is perpendicular to the tangent line at the point of tangency Write an equation of the normal line at x = 1

Find f ’(x).

Use the limit process to determine the slope of the tangent line to f(x) at x = 5. Write an equation of the tangent line to the graph of f at the indicated point, confirm your answer using your calculator. Write an equation of the normal line to the graph of f at the indicated point.