States that if a real-valued function f is continuous in the closed and bounded interval [a,b], then f must attain its maximum and minimum value, each at least once.
What is Extreme Value Theorem?
100
Name the derivative of ∫ f'(x)
What is f(x) ?
100
The derivative of 1/2x²
What is x
100
The integral of x2
What is (1/3)x3
200
Implies f is concave down
What is f"<0?
200
States that a differentiable function which attains equal values at two distinct points must have a point somewhere between them where the first derivative is zero.
What is Rolle's Theorem?
200
The derivative of 2x(cos(3x))
What is 2cos(3x)(-3sin(3x))
200
The derivative of y=(x1/2)(tan x).
What is What is 2x-1/2tan x + x1/2sec2x?
200
The integral of 4x3+8x+2
What is x4+4x2+2x
300
The inflection points of y = x4 + 6x2 - 9.
What is x = 1 and x = -1?
300
Shows that an indefinite integration can be reversed by a differentiation. i.e. The derivative of the integral of f(x) is equal to f(x)
What is The First Fundamental Theorem of Calculus?
300
The derivative of e4x
What is 4e4x
300
Evaluate using the quotient rule: f(x)=3x/5x3
What is (15x3-45x3)/25x6
300
The integral of -sin x
What is cos x
400
The interval upon which y = ex + x is concave up.
What is (-∞,∞)?
400
Allows one to find the definite integral of a function by using any one of its infinitely many antiderivatives. i.e. the integral from a to b of f(x) equals g(b)-g(a), such that f(x)=g'(x)
What is Second Fundamental Theorem of Calculus?
400
Name the derivative of ln (sec x +tan x)
What is sec x ?
y = ln (sec x + tan x )
dy/dx = (sec x tan x + sec2 x)/(sec x + tan x)
= sec x ( sec x + tan x) / (sec x + tan x)
= sec x
400
The derivative of y=(x1/2)(tan x).
What is 2x-1/2tan x + x1/2sec2x?
400
The integral of cos(2x)
What is (sin x)(cos x)
500
Discuss the concavity of the function. f(x)=(x+3)1/2 * x
What is concave upward: (-3, infinity)?
500
States that given a curve between two endpoints, there is at least one point at which the tangent to the curve is parallel to the line through its endpoints.