Lesson: Critical Points and Local Extrema of a Function Mathematics • 12th Grade

In this lesson, we will learn how to find critical points of a function and check for local extrema using the first derivative test.

Lesson Plan

Students will be able to

recall the definition of a critical point of a function,
find the critical points of a function,
understand that critical points can be classified as minima, maxima, and points of inflection,
classify a critical point as a local minimum or maximum using the first derivative test.

Q1:

Determine the number of critical points of the following graph.

Q2:

Determine the critical points of the function in the interval .

Q3:

Which graph has three real zeros and two local maxima?