1. Today in Calculus Go over homework Derivatives by limit definition Power rule and constant rules for derivatives Homework

2. When f′(a) fails to exist Where the tangent does not exist: points of discontinuity (function does not exist) at corners at cusps Also at vertical tangents (slope is undefined)

3. Theorems If f has a derivative at x = a, then f is continuous at x = a. Intermediate Value Theorem for derivatives: If a & b are any two points in an interval on which f is differentiable, then f ′ takes on every value between f ′(a) & f ′(b).

4. Note: A function can be continuous but not differentiable but if it is differentiable it has to be continuous

5. Finding the Derivative

8. Derivative Rules Power rule: f(x)f′(x) 3x 7x x2x2 x3x3

9. Derivative Rules Sum and difference rules: If u and v are differentiable functions of x, then f(x)= 3x 2 +5x – 12

10. Examples