Calculus Questions
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f11x--- points of inflection on f(x)
f1x --- Max/min of fx, slope of fx is 0
If a > 0, then v is ___; and if a < 0, then v is ___.
Rolle's Theorem:Let f be a continuous on the closed interval [a, b] and differentiable on the open interval (a, b). If f(a) = f(b), then:
T/F Differentiability implies continuity.
The derivative of an inverse function:If f has an inverse function g, theng'(x) =
Right Circular CylinderLateral Surface Area =
If a and v are both opposite signs, then the speed of P is ___ or P is ___.
Cone(A = Area of the base)Volume =
If s is a continuous function of t, then P reverses direction whenever v is ___ and a is ___; note that zero velocity does not necessarily imply a ___ in direction.
Alternate Form of the Derivativelim x->c [f(x) - f(c)]/x-c
If v < 0, then P is moving to the ___ and its distance s is ___.
First Fundamental Theorem of Calculus:If a function f is continuous on the closed interval [a, b] and F is an antiderivative of f on the interval [a, b], then:
Second Fundamental Theorem of Calculus:If f is continuous on an open interval I containing a, then, for every x in the interval:
Mean Value Theorem (for derivatives) (MVT):If f is continuous on the closed interval [a, b] and differentiable on the open interval (a, b), then:
Extreme Value Theorem (EVT):If f is continuous on the closed interval [a, b], then:
What is the average rate of change of a function f on an interval [a, b]?
Intermediate Value Theorem (IVT):If f is continuous on the closed interval [a, b] and k is a number between f(a) and f(b), then:
Average Value of a Function on an Interval:If f is integrable on the closed interval [a, b] then the average value of f on the interval is:
T/F Continuity implies integrability.