DIFFERENCE QUOTIENT, DERIVATIVE RULES, AND TANGENT LINES RIZZI – CALC BC

Find the derivative of f using the definition of the derivative REVIEW – DERIVATIVE BY LIMIT PROCESS

DIFFERENTIABILITY Means you can take the derivative at any point (ie, you can find slope anywhere) Which of the following are differentiable?

EXAMPLE 1 – DIFFERENTIABLE?

EXAMPLE 2 – DIFFERENTIABLE?

EXAMPLE 3 – DIFFERENTIABLE?

EXAMPLE 4 – DIFFERENTIABLE?

DIFFERENTIABLE VS CONTINUOUS  Can a function be continuous but not differentiable?  Can a function be differentiable but not continuous?

DERIVATIVE RULE SHORT CUTS – PART 1 Power Rule  Remember: the derivative is a rule for the slope of the function at EVERY point

FINDING SLOPE OF A GRAPH  Find the slope of the graph of f at the following x values: a.x = -1 b.x = 0 c.x = 1

FINDING AN EQUATION OF A TANGENT LINE  Find an equation of the tangent line to f when x = -2  To find equation of a line, we need 2 things:

DERIVATIVE RULE SHORT CUTS – PART 2 Sine and Cosine Rules  Remember: the derivative is a rule for the slope of the function at EVERY point

PRACTICE FREE RESPONSE QUESTION