Analysis

Quick Notes

These are the problems where you are given a function (often in the form of a graph or table) and asked to determine information about related functions.
There is always an analysis FRQ on both the AB and BC exams, and it is usually non-calculator.
Usually the function you are given will be a derivative, and you will be asked questions regarding the original function. This may involve integrating using geometric area.
These questions are usually non-calculator.
Features you need to know include:

intervals of increase and decrease

concavity

relative (or absolute) maximums and minimums

critical values

points of inflection

Be prepared to find function values and/or slopes, and you may need to write the equation of a tangent line or perform a tangent line approximation.
Remember that horizontal tangent lines have a slope of 0, and vertical tangent lines have an undefined slope.
FTC is often involved with these problems.
The existence questions ("does there exists", "must there be", etc.) are common and involve either IVT or MVT (see Reference Sheet below).
Remember to ALWAYS JUSTIFY your statements using calculus (see Reference Sheet below).
Be careful with notation.

~ Related CED Units ~ 3, 4, 5, 6, 8

FRQ Samples