Extrema

Front

What is an extremum in calculus?

Back

An extremum is a point in a function where the function reaches a local maximum or minimum value.

Front

Define local minimum.

Back

A local minimum is a point where the function value is lower than all nearby points.

Front

Define local maximum.

Back

A local maximum is a point where the function value is higher than all nearby points.

Front

What does the first derivative test determine?

Back

The first derivative test determines whether a critical point is a local maximum, local minimum, or neither.

Front

What is a critical point?

Back

A critical point is a point in the domain of a function where the derivative is zero or undefined.

Front

How do you find local extrema using the first derivative?

Back

1. Find the derivative of the function. 2. Set the derivative equal to zero to find critical points. 3. Use the first derivative test to classify each critical point.

Front

What does it mean if f'(x) > 0 on an interval?

Back

If f'(x) > 0, the function f(x) is increasing on that interval.

Front

What does it mean if f'(x) < 0 on an interval?

Back

If f'(x) < 0, the function f(x) is decreasing on that interval.

Front

What is a sign chart?

Back

A sign chart is a visual representation that shows the intervals where a function is increasing or decreasing based on the sign of its derivative.

Front

How can you determine the number of extrema from a sign chart?

Back

Count the number of times the sign of the derivative changes from positive to negative (local maxima) or negative to positive (local minima).