What Derivatives Tell Us
A point that is a candidate for a maximum or minimum of a function.
What is a critical point?
The radius of the unit circle.
What is 1?
This rule can be used to evaluate the derivative on any variable raised to a non-zero power.
What is the power rule?
A famous euclidean geometry theorem for finding right triangle side lengths.
What is the Pythagorean Theorem?
The goal of optimization.
What is to maximize or minimize?
A point that marks when a function's slope changes from increasing or decreasing.
What is an inflection point?
An expression used to find the area of a circle.
pi*r^{2}
Derivatives for the products of two functions could require the use of this rule.
What is the product rule?
Relates the slope of the secant line on an interval to the slope of the tangent line.
What is the Mean Value Theorem?
A relation that results from the conditions in the problem statement.
What is a constraint?
It's indicated by a positive value for the second derivative.
What is concave up?
The derivative of the area of a circle.
What is the circumference of a circle?
A rule used to differentiate rational functions.
What is the quotient rule?
One of its conditions is f(a) = f(b).
What is Rolle's Theorem?
A potential name for the function we seek to maximize/minimize.
What is the objective function?
The highest or lowest value for a function on a closed interval.
What is an absolute maximum or minimum?
These two functions relate the opposite and adjacent sides of a right triangle.
What are tangent and cotangent?
A rule defined by function composition.
What is the chain rule?
An existence theorem that guarantees an absolute maximum and minimum occurs on an interval.
What is the extreme value theorem?
A type of tangent line that could occur when the derivative is undefined.
What is a vertical tangent line?
2*pi*r^{2} + 2*pi*r*h
What is the surface area of a cylinder?
This handy derivative rule lets us factor out constants and multiply after taking derivatives instead.
What is the constant multiple rule?
Not a theorem at all: a list of four different ways of writing the derivative given y = f(x).
dy/dx, df/dx, y', f'(x)