What the derivatives of a function tell us about the shape of its graph

Proving and then applying the Fundamental Theorem of Calculus

Mean Value Theorem and using derivatives to find the shape of curves

Mean Value Theorem and using derivatives to find the shape of curves

Determining the properties of a function from the graph of its derivative

Finding where a function is increasing, decreasing, concave up and concave down and its local extrema and inflection points

Finding where a function is increasing, decreasing, concave up and concave down and its local extrema and inflection points

Finding where a function is increasing, decreasing, concave up and concave down and its local extrema and inflection points

Sketching a curve given information about the function and its derivatives