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.

Instructions

Work on

4.5: 195, 197, 201-209 odd, 213, 225-229 odd, 237

Participate Chapter 4 Discussion for questions and answers.
Keep notes for main concepts, problems you struggled with and your reflection etc.
Contact me if you have any questions.

Videos

Finding decreasing interval given the function $f (x) d e c r e a s i n g ⟹ f^{'} (x) < 0$		Finding increasing interval given the derivative $f (x) i n c r e a s i n g ⟹ f^{'} (x) > 0$
Concavity introduction		Inflection points introduction
Analyzing concavity (graphical)		Analyzing concavity (algebraic)
Inflection points (graphical)		Inflection points (algebraic)
Mistakes when finding inflection points: second derivative undefined		Mistakes when finding inflection points: not checking candidates
Second derivative test		Connecting $LaTeX: f\left(x\right),\:f\:'\:\left(x\right),\:f\:''\left(x\right)$ graphically