What weren't we allowed to use on tests?
The instantaneous rate of change will equal the mean rate of change somewhere in the interval
mean value theorem
a line that intersects a curve only once
tangent line
the slope of a tangent line
the slope of a vertical line
the rate of change with respect to x
a line segment intersecting two lines
secant lines
the relative maximum and minimum points of the parent function
critical point
tells us max/min, increasing/decreasing intervals, slope of tan line, velocity
first derivative test
when the function changes concavity
inflection point
the derivative of speed
the derivative of velocity
rate at a specific moment
instantaneous rate
where does a derivative not exist
the rate over a time interval
average rate of change
the absolute value of velocity
what is it called when velocity is moving backwards
negative velocity
how can you tell if a function is concave up or down
second derivative test
the lowest point of a function
absolute minimum
a line or curve that the graph follows closely but never touches
the highest point of a function
absolute maximum
when there is a range on a function or set of numbers
an interval that contains its endpoints
closed interval
when the graph of a function is continuous
a function that moves upward from left to right
increasing function
a function obtained by switching the x and y variables in a function
inverse function
does not include its endpoints
open interval
the set of x-values for which a functon is defined
rates if change are related by differentiation
related rates