Chapter 5.

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Presentation transcript:

Chapter 5

If is decreasing then ...

If is decreasing, then …

For what kind of function would a tangent line approximation be LESS THAN the original function?

If is concave up then …

An inflection point occurs at a point in the domain when ______.

If is increasing then ...

If is concave down then …

Instantaneous Rate of Change. = Which Theorem does this describe? Average Rate of Change Instantaneous Rate of Change. =

If has an inflection point, then …

If _____ and ______ then has a relative minimum at x = a.

If is increasing, then ...

If has a horizontal tangent at x = a then ...

What does the mean value theorem (MVT) tell us?

When identifying absolute extrema on a closed interval, compare the y-coordinates of the ______ and ______.

For what kind of function would a tangent line approximation be GREATER THAN the original function?

A maximum point occurs when _______.

is concave down when ______.

If has a relative extrema then ...

If _____ and ______ then has a relative maximum at x = a.

A maximum point occurs when ________.

Which Theorem does this describe? Slope of Secant Line Slope of Tangent Line =

is concave up when ____________.

A minimum point occurs when ________.

An inflection point occurs when ________.

is concave up when _______.

Calculating the time when the average velocity equals the instantaneous velocity is an application of __________.

A minimum point occurs when ________.

is concave down when ________.

If the graph of has an extrema at x = b, then the graph of has a(n) _________ at x = b.