Concavity Flashcard

Front

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

Back

There is a local maximum.

Front

At what x-value does f have a relative minimum if f' changes sign?

Back

x = -3.

Front

How do you determine the intervals where f(x) is decreasing?

Back

Identify where f'(x) is negative.

Front

What are the intervals of concavity for f(x) = x^2 + 2x + 1?

Back

Concave up: (-∞, ∞).

Front

What does a sign chart for f'(x) help identify?

Back

It helps determine local extrema.

Front

What is the definition of concavity in calculus?

Back

Concavity refers to the direction of the curvature of the graph of a function.

Front

How do you find inflection points?

Back

Inflection points occur where the second derivative changes sign.

Front

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

Back

The function f(x) is concave up on that interval.

Front

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

Back

The function f(x) is concave down on that interval.

Front

What is the relationship between f'(x) and f(x) in terms of increasing and decreasing?

Back

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