anti-f
This is the proper function notation for an Antiderivative
What is F(x)?
xn+1 = xn - f(xn)/f'(xn)
After f'(x) crosses above the horizontal axis, we can state that f(x) would be ______
What is Increasing
What is f(x) is continuous, differentiable, and f(a) is equal to f(b)
Using this first equation, one may find the desired equation used in optimization
What is the Secondary/Constraint Equation?
This implied variable is added in antidifferentiation.
What is "C"?
This button is useful for storing variables when applying Newton's Method using a calculator
What is STO->
The concavity on an interval is ____ when f''(x) is less than zero
This formula can be used to prove the Mean Value Theorem
What is f'(c) = f(b) - f(a) divided by b - a
Once an equation has a single variable objective it is optimized by doing this process
What is taking the derivative, setting equal to zero, and solving for the variable?
The derivative of arctanx + C
What is 1/(1+x^2)dx
After this occurs, it is okay to stop approximating for xn
What is successive approximations agreeing to the 8th decimal place?
The derivative of a function x is greater than zero on the interval (-10, 1) and less than zero on the interval (1,10), which tells us f(x) is ______ and _____ across these intervals.
What is Increasing and Decreasing
By Rolle's Theorem, there exists a value C which the derivative of the function equals this
what is zero
What is pi*r2 + 2pi*r*h
This antiderivative requires the absolute value of x
What is ln|x| + C?
Netwon's Method uses approximations to find this value on a graph
What is the root r, or the X-Intercept?
These important numbers are found when f'(x) equals zero or does not exist.
What are critical numbers
With the Mean Value Theorem we are able to determine this about the tangent line at f(c)
A box with square ends, x, length, y, and Perimeter P would have this primary equation for its volume after substituting y.
What is V = x2P - 4x3
These steps are taken to find the origin of an object when given the rate of change in velocity
What is taking the antiderivatives of Acceleration and Velocity
Under these circumstances, Newton's approximation seems to fail
What is when f'(x1) near zero?
When the second derivative changes signs, there are one of these present
What is Inflection Point
The corollary example f(x) = g(x) + c while f'(x) is equal to g'(x) is useful when finding this
What is the Antiderivative
This formula is useful for minimizing distance from a given point on a graph
What is d = Sqrt(x2-x1)2 + (y2-y1)2