When the limit value of a function equals the function value
The _______ derivative test states that if f' changes signs at a critical number, then f has a relative extrema at the critical number.
The slope of the tangent line to a curve
An interval that contains its endpoints.
A value of x at which the derivative is either 0 or undefined. (2 words)
Obtaining the derivative of a function.
A limit whose value cannot be found by direct substitution (e.g. 0/0)
An ______ point is where the concavity changes.
Finding the best possible outcome from a set of available outcomes
_________ derivative is related to concavity
______ maximum. The highest point of a function.
When the left and right limits at a point are two different numbers, the function has a ______ discontinuity
Down
A part of the graph that looks like a frown
A place where f'(x)=0, but f' does not change signs.
The ________ derivative test uses concavity at critical numbers to determine if critical numbers are maximums or minimums.
The value that a function approaches as the domain variable approaches a specific value.
When the first derivative is positive, the function is _______
A function whose derivative can be found everywhere is ________
The rate of change of velocity over time
When f'<0, then f is _________
A point where the graph has a peak or a valley. (2 words)
The rate of change in the position of an object.
When a function is always trapped between two numbers.
-discontinuity. Hole in the graph
A line or curve that the graph gets really close to.
When f''>0, then f is _______ ______
-rule. Finding the derivative of the numerator and denominator to evaluate the limit of a function.
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