Warm Ups. AP Calculus 3.1 Tangent Line Problem Objective: Use the definition to find the slope of a tangent line.

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Presentation transcript:

Warm Ups

AP Calculus 3.1 Tangent Line Problem Objective: Use the definition to find the slope of a tangent line

History Calculus grew out of 4 major problems Tangent Line Problem Fermat (1601 – 1665) Descartes (1596 – 1650) Huygens (1629 – 1695) Barrow (1630 – 1677) Newton ( ) Leibniz ( )

Slope of a Secant line

Slope of a tangent line

Example

Definition of a derivative

Find the derivative of… f(x) = x 3 + x 2 f’(x) =

Find the equation of a line Find the equation of the line tangent to the function f(x) = x 2 + 2x + 1 at the point (-3, 4).

Differentiability A function is not differentiable at c if the function is not continuous at c f(x) = [x] the limits are not the same on both sides of c (sharp point) f(x) = |x| tangent line is vertical at c f(x) = x 1/3

Assignment Page 1245 – 33 eoo, 37 – 40, 57