AP CALC AB UNIT 5

The points of inflection for f are what of f’ and f’’?

Relative Extrema for f’ and zeros of f’’

What is the mean value theorum?

If a function is continuous on the closed interval [a,b] and differentiable on an open interval (a,b) then there is an x value where the IROC is equal to the AROC

How to use MVT

Find the x value where the IROC is equal to the AROC using the given interval/points to find AROC and then use that value to solve for x of IROC

If f is concave up then…

f’ is increasing through the x-axis and f’’is positive

If f is concave down then f’ is…

Decreasing through the x-axis

If f is concave down the f’’ is…

Negative

What is the Extreme Value Theorum

If a function is continuous on the closed interval [a,b] then there has to be exactly on max and one min.

Relative (local) extrema is when…

The function is on an open interval, has no clear max or min.

Absolute (global) extrema is when…

The function is on a closed interval, has one max and one min.

A Critical Point is…

A point where f’ (c) =0 or f’(c) is undefined

The Candidates test is when…

You find critical points and then plug them into f(c), whichever y value is the highest/lowest is where the extremum’s are. Must be on a closed interval.

First Derivative test is when…

You take the first derivative, set equal to zero. Make table to test where the (relative) max/mins of f happen. Can be used on an open interval or closed interval.

The critical points of a derivative of a function are the blanks for the original function

Points of inflection

What is optimization looking for?

Maximums and minimums

How do you find maxes/mins for optimization?

When f’(x)=0 or where it fails to exist, and endpoints. Take volume (or other equation), find derivative, set equal to zero, make table, find maxes/mins that is the max/min amount the thing can hold