Section 4.5 Derivatives and the Shape of a Graph

Text for Section 4.5 Derivatives and the Shape of a Graph

Learning Objectives

• Explain how the sign of the first derivative affects the shape of a function’s graph.
• State the first derivative test for critical points.
• Use concavity and inflection points to explain how the sign of the second derivative affects the shape of a function’s graph.
• Explain the concavity test for a function over an open interval.
• Explain the relationship between a function and its first and second derivatives.
• State the second derivative test for local extrema.

• Finding intervals of increasing/decreasing
• Finding intervals of increasing/decreasing with trig functions
• The first derivative test for relative/local extrema
• Determining Concavity
• More examples of concavity with trig functions
• The second derivative test
• Second derivative test with trig functions