Vocab
This term describes a line which touches a function at one point and has the same slope as the function at that point.
What is a tangent line?
This function is the derivative of ln(x2+1).
What is 2x / x2+1 ?
This problem type involves two or more rates of change which are connected by some central equation.
What is a related rates problem?
A function is concave down when this condition is true.
What is when the second derivative is negative? (or the first derivative is decreasing)
[SLIDE 1]
What is the derivative of ex = ex ?
This type of value represents the x-values at which a function's derivative equals zero, or is undefined.
What is a critical value?
This expression would represent the antiderivative of f'(3x).
What is (1/3)f(3x)+C ?
This strategy is used to find the absolute maximum or minimum of a function between two given values.
What is the Closed Interval Method?
When the first derivative changes from increasing to decreasing, this occurs on the parent function.
What is an inflection point?
[SLIDE 2]
What are one-sided limits?
This term refers to the part of a function which is inside an integral.
What is the integrand?
1/x is the antiderivative of this function.
What is -1/x2 ?
When solving a Riemann sum, one should annotate 1) the interval of the area, 2) the number of subintervals, and 3) this important given.
What is the type of Riemann sum?
What is a hole (or removable discontinuity)?
[SLIDE 3]
DAILY DOUBLE!
What is the use of the second derivative test to classify critical points as maxima or minima?
This term refers to a point where a function is continuous, but not differentiable.
What is a cusp?
This function is the 16th derivative of cos(x).
DAILY DOUBLE!
What is cos(x)?
This information is required to justify use of L'Hopital's rule.
What is the limit of both the numerator and denominator of a function approaching 0 or infinity?
This statement would justify that a function f has a minimum at a certain value x = a.
What is f' changes from negative to positive at x = a, or f''(a) < 0 ?
[SLIDE 4]
What is the first integral can be solved with u-substitution, whereas the second cannot?
This is the name for a function that satisfies a differential equation with a given initial condition.
What is a particular solution?
This would be the area under the graph of 1/x between [-1,1].
What is undefined?
When a region is rotated around a vertical line, this technique would be used to find the volume of the solid.
What is the washer method, integrating with respect to y?
This condition will result in a right Riemann sum being an underestimate.
What is a strictly decreasing function?
[SLIDE 5]
What is that a Riemann sum is approximate area, but an integral is exact area?