First Derivative Test

Front

What does it indicate if f'(a) = 0 and f'(x) changes from positive to negative at x = a?

Back

f(x) has a relative maximum at x = a.

Front

At what x-value does f(x) have a minimum if it is given that f'(x) changes sign?

Back

x = 5.

Front

What can be determined from the sign chart of f'(x)?

Back

There is a local maximum at x = -2 and a local minimum at x = 4.

Front

What test is used to check for sign changes at the critical points of a function?

Back

1st Derivative Test.

Front

How is the slope of a function described?

Back

By its first derivative.

Front

What is a critical point in the context of the first derivative test?

Back

A point where f'(x) = 0 or f'(x) is undefined.

Front

What does a positive first derivative indicate about the function f(x)?

Back

The function is increasing.

Front

What does a negative first derivative indicate about the function f(x)?

Back

The function is decreasing.

Front

What is the relationship between the first derivative and local extrema?

Back

Local extrema occur at critical points where the first derivative changes sign.

Front

What is the significance of the first derivative test in calculus?

Back

It helps determine whether a critical point is a local maximum, local minimum, or neither.