First derivative test relative extrema and increasing decreasing intervals

The video tutorial covers the basics of derivatives, focusing on continuity and critical values. It explains the application of the product rule to find derivatives and identifies critical values in a function. The tutorial further analyzes function behavior, emphasizing the importance of understanding critical points. Finally, it discusses determining intervals and identifying local minima, providing a comprehensive understanding of these calculus concepts.

What is a critical value in the context of derivatives?

• A point where the function is undefined

• A point where the derivative is zero or undefined

• A point where the function has a maximum value

• A point where the function is continuous

Which rule is used to find the derivative in the given example?

• Product Rule

• Power Rule

• Chain Rule

• Quotient Rule

When solving a rational function, what should you set to zero to find critical values?

• The entire function

• The denominator

• The derivative

• The numerator

Why is x=0 considered a critical value in the example?

• Because the function is continuous at x=0

• Because the derivative does not exist at x=0

• Because the function has a maximum at x=0

• Because the function is undefined at x=0

What is the significance of a local minimum in a function?

• It is the point where the derivative is maximum

• It is the point where the function is undefined

• It is the point where the function changes from decreasing to increasing

• It is the highest point in a given interval

How do you determine if a function is increasing or decreasing in an interval?

• By using test points in the interval

• By finding the maximum value in the interval

• By evaluating the function at the endpoints

• By checking the sign of the second derivative

What does it mean if a function's derivative changes from negative to positive?

• The function has a local maximum

• The function is undefined

• The function has a local minimum

• The function is constant