Connecting f, f', and f''

Front

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

Back

The function f(x) is decreasing at that interval.

Tags

CCSS.HSF.LE.B.5

Front

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

Back

The function f(x) is increasing at that interval.

Tags

CCSS.HSF.IF.B.4

Front

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

Back

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

Tags

CCSS.HSF.LE.B.5

Front

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

Back

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

Tags

CCSS.HSF.LE.B.5

Front

What is a local maximum?

Back

A point where the function changes from increasing to decreasing.

Front

What is a local minimum?

Back

A point where the function changes from decreasing to increasing.

Front

What is a point of inflection?

Back

A point where the function changes concavity.

Tags

CCSS.HSF-IF.C.7A

Front

If f' is positive and decreasing, what can be inferred about f?

Back

f is increasing but at a decreasing rate.

Tags

CCSS.HSF.LE.B.5

Front

If f' is positive and increasing, what can be inferred about f?

Back

f is increasing at an increasing rate.

Tags

CCSS.HSF.LE.B.5

Front

If f' is negative and increasing, what can be inferred about f?

Back

f is decreasing but at a decreasing rate.

Tags

CCSS.HSF.IF.B.4