Derivative Graphs

F(x) increasing/decreasing

Rising and falling slope

F(x) Absolute Max/min

Highest/lowest X value can be end points

F(x) critical numbers

Where slope is horizontal (often peak and trough)

F(x) Concave up/down

Look at shape

F(x) Inflection point

The point where graph changes to concave up to concave down

F’(x) In increasing/decreasing

Above X axis increasing

Below X access decreasing

F’(x) Relative max/minimum

Max is positive to negative Y value

Minimum is negative positive Y value

F’(x) Critical numbers

X intercept Y equals zero

f’(x) concave up/down

Look at increasing or decreasing slope

F’(x) Inflection point

Point where graph changes from increasing to decreasing

F”(x) Concave up/down

Down when Y values negative

Up when Y values positive

F”(x) Inflection point

X equals zero and sign changes

When do you use brackets in your answer?

For increasing and decreasing

When do you use parentheses in your answer?

When talking about concavity