Given the derivative graph of f' find the relative min

The video tutorial explains how to identify local minima and maxima by analyzing the graph of the derivative function, F prime of X. It discusses the importance of slope changes, particularly from negative to positive, in determining local minima. The tutorial also covers how to find critical values by setting the first derivative to zero and examines specific examples to illustrate these concepts.

What does a change from a negative slope to a positive slope indicate about a function?

• No change in the function

• A point of inflection

• A local minimum

• A local maximum

How do you find critical values of a function?

• By setting the second derivative to zero

• By finding the X-intercepts of the original function

• By setting the first derivative to zero

• By finding the Y-intercepts of the derivative

At X equals -5, what type of extremum is present?

• A point of inflection

• No extremum

• A local maximum

• A local minimum

What is the behavior of the slope at X equals 5?

• Changes from negative to positive

• Remains positive

• Changes from positive to negative

• Remains negative

Which X value is associated with a local minimum?

• X equals 5

• X equals -5

• X equals -1

• X equals 0