Learn how to find relative extrema and justify using first derivative test

The video tutorial covers identifying relative maxima and minima of a polynomial function. It begins by discussing the continuity of the function and finding critical values through derivatives. The first derivative test is used to determine whether these critical points are maxima or minima by analyzing slope changes. The tutorial explains how to justify these findings and identifies intervals where the function is increasing or decreasing.

What is the first step in finding the critical values of a polynomial function?

• Evaluate the function at endpoints

• Set the function equal to zero

• Take the derivative and set it to zero

• Find the second derivative

What does the first derivative test help determine about a function?

• The concavity of the function

• Whether critical points are relative maxima or minima

• The continuity of the function

• The absolute maximum and minimum

When analyzing the function's behavior around critical points, what is the significance of a positive to negative slope change?

• It indicates a local minimum

• It indicates a local maximum

• It indicates a point of inflection

• It indicates the function is constant

Which value is used to test the behavior of the function to the left of zero?

• 1

• -1

• 2

• 0.5

What is the importance of explaining the reasoning behind identifying local maxima and minima?

• To ensure the function is continuous

• To determine the function's domain

• To justify the use of the first derivative test

• To find the absolute extrema

What intervals is the function increasing on, according to the instructor?

• From 0 to infinity

• From negative infinity to 0 and from 1 to infinity

• From 0 to 1

• From negative infinity to 1

What is the function's behavior between zero and one?

• The function has a point of inflection

• The function is decreasing

• The function is increasing

• The function is constant