Extrema and Concavity

Front

What occurs when f'(x) changes from negative to positive?

Back

There is a minimum.

Front

The concavity of a function is described by its _____________.

Back

second derivative.

Front

If (a,b) is a local minimum, what is true about f'(a)?

Back

It's zero.

Front

What does the sign chart for f'(x) indicate if there are no extrema?

Back

There are no local maxima or minima.

Front

Over what interval(s) is the particle moving left if the velocity function indicates negative velocity?

Back

(3, 8).

Front

What is the first derivative test used for?

Back

To determine local extrema of a function.

Front

What does a positive second derivative indicate about a function's concavity?

Back

The function is concave up.

Front

What does a negative second derivative indicate about a function's concavity?

Back

The function is concave down.

Front

What is the relationship between inflection points and concavity?

Back

Inflection points occur where the concavity changes.

Front

How can you determine if a critical point is a local maximum or minimum?

Back

By using the first derivative test.