Concavity Flashcard

Front

What does it indicate when f'(x) changes from positive to negative?

Back

There is a maximum.

Front

What is the interval where f(x) is concave up if f' is graphed?

Back

(-∞,-3) U (1, ∞)

Front

At what x-value does f have a relative minimum based on the graph of f'?

Back

x=-3

Front

What describes the concavity of a function?

Back

The second derivative.

Front

Identify the interval from the derivative graph where the function is concave up.

Back

(-1,1) & (3,4)

Front

What is the relationship between the first derivative and increasing/decreasing functions?

Back

If f'(x) > 0, then f(x) is increasing; if f'(x) < 0, then f(x) is decreasing.

Front

How can you determine points of inflection?

Back

Points of inflection occur where the second derivative changes sign.

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 significance of a zero second derivative?

Back

It may indicate a point of inflection, but further analysis is needed.