positive
When f is increasing, f' is
negative
When f is decreasing, f' is
increasing
When f is concave up, f' is
decreasing
When f is concave down, f' is
positive
When f is concave up, f" is
negative
When f is concave down, f" is
zero or is undefined
When f has a critical point, f' has a
extrema
When f has an inflection, f' has an
zero
When f has an inflection, f" has a
critical point
when the derivative is zero or undefined
Mean Value Theorem
Says that the graph of a continous and differential function has a secant line that equals the tangent line at some point or points on an interval.
Extreme Value Theorem
Says that a continuous function must have an absolute maximum point and minimum point over the interval [ a , b ]
First Derivative Test
Finds possible extrema, increasing and decreasing intervals of a function.
Second Derivative Test
Finds inflection points and concavity of a given function
Derivative does not exist
at points on a graph where there is asymptotes, holes, jump discontinuity, infinite oscillations, cusp or corner.
Slope of the tangent line
Instantaneous rate of change or derivative
Slope of the secant line
average rate of change or slope
velocity
the derivative of distance over time
acceleration
the derivative of velocity or the second derivative of distance over time
increasing
When f' is positive, f is
decreasing
When f' is negative, f is
extrema
When f' crosses the x-axis, f has a/an
concave up
When f" is positive, f is
concave down
When f" is negative, f is
inflection
When f" crosses the x-axis, f has a/an