Theorems
Derivatives
Integrals
History
Random
100
What theorem states that if a continuous function takes on two values y1 and y2 at points a and b, it also takes on every value between y1 and y2 at some point between a and b
What is Intermediate Value Theorem (IVT)
100
State the Product Rule
What is (fg)′=f′g+fg
100
A synonym for integral that starts with "a"
What is an anti derivative
100
The mathematician from England credited for developing calculus.
Who is Isaac Newton?
100
When f prime changes from positive to negative
What is a critical value?
200
What theorem states that if a function f(x) is continuous on a closed interval [ a, b], then f(x) has both a maximum and minimum value on [ a, b]
What is Extreme Value Theorem
200
State the Quotient Rule
What is (f/g)' = (f'g-fg')/g^2
200
The integral of (1/x)
What is ln(x) + C
200
Newton applied calculus to majorly this science
What is physics?
200
A function has to be this in order to be differentiable
What is continuous?
300
What theorem states that if a function f is continuous on the closed interval [a, b] and differentiable on the open interval (a, b) such that f(a) = f(b), then f′(x) = 0 for some x with a ≤ x ≤ b
What is Rolle's Theorem
300
State the derivative of csc(x)
What is (-csc(x))(cot(x))
300
If you want to find the area underneath a graph from (a,b) you would use what type of integral?
What is a definite integral
300
The mathematician from Germany credited for developing calculus.
Who is Gottfried Leibniz?
300
Type of line that passes through a function at x=a and has a slope m=-1/f'(a)
What is a Normal Line
400
What theorem states that if f is a continuous on [a,b] and differentiable on (a,b), then there exists a number c in (a,b) such that
What is Mean Value Theorem (MVT)
400
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400
The easiest method to use to integrate (x^2)(e^x)
What is the tabular method?
400
The word "calculus" originates from this language.
What is Latin?
400
A y-value that a function approaches from either side of a certain x-value
What is a limit?
500
What theorem states if f is continuous on an open interval containing a, then for every x in the interval the derivative of the the integral of f(x) dx on said interval is equal to f(x)
What is the Second Fundamental Theorem of Calculus
500
A function that models the slope of the curve for all x-values for which it exists. This is the definition of what?
What is the definition of a derivative
500
The definite integral of what function gives you the distance a particle has traveled?
What the absolute value of the velocity function.
500
Newton invented calculus to solve this problem.
What is describing a falling object at any given time?
500
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State the Pathegorian Identity
(sinx)^2+(cosx)^2=1