Using the First Derivative Test in Calculus

Front

What does the First Derivative Test help determine?

Back

The First Derivative Test helps determine the intervals where a function is increasing or decreasing, as well as identifying local maxima and minima.

Front

If f'(x) > 0, what can we say about f(x)?

Back

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

Front

If f'(x) < 0, what can we say about f(x)?

Back

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

Front

What is a critical point in the context of calculus?

Back

A critical point is where the first derivative f'(x) is either zero or undefined.

Front

What is the significance of a sign change in f'(x) at a critical point?

Back

A sign change in f'(x) at a critical point indicates a potential local maximum or minimum.

Front

What does it mean if f'(x) changes from positive to negative at a critical point?

Back

If f'(x) changes from positive to negative at a critical point, it indicates a local maximum.

Front

What does it mean if f'(x) changes from negative to positive at a critical point?

Back

If f'(x) changes from negative to positive at a critical point, it indicates a local minimum.

Front

What is the relationship between the first derivative and the slope of a function?

Back

The first derivative of a function represents the slope of the function at any given point.

Front

What is the First Derivative Test used for?

Back

The First Derivative Test is used to determine the behavior of a function at critical points and to find local extrema.

Front

How do you find intervals of increase and decrease using the First Derivative Test?

Back

To find intervals of increase and decrease, determine where f'(x) is positive (increasing) and where f'(x) is negative (decreasing).