If f(x) is continuous on the closed interval [a,b] and differentiable on the open interval (a,b), then there exists a number c in (a,b) such that f`(c) = f(b) - f(a) / b - a

The derivative of f(x) = c where c is a constant is given by f'(x)=0

A function is what if you can take its derivative at every point

If f(x) is continuous on an open interval I containing a, then, for every x in the interval, d / dx integral a to x f(t) dt = f(x)
If f(x) is continuous on the closed interval [a,b], and F(x) is an antiderivative of f(x) on the interval [a,b], then integral a to b f(x) d(x) = F(b) - F(a)
The total change theorem says: F(b) = F(a) + integral a to b f(x) dx

The derivative of f(x) = g(x) / h(x) is given by f '(x) = ( h(x) g '(x) - g(x) h '(x) ) / h(x) 2

A function that models the slope of the curve for all x-values for which it exists

let f(x) be a function continuous on the closed interval [a,b]. If N is any real number between f(a) and f(b), then there is at least one real number c between a and b such that f(c)=N

The limit of f(x)/g(x) is the same as the limit of f'(x)/g'(x)

The line that is perpendicular to the tangent line at the point of tangency

If P(x) is a polynomial of degree n, with complex coefficients, then the equation P(x) = 0 has exactly n roots

The derivative of f(x) = x r where r is a constant real number is given by f '(x) = r x r - 1

∫_a^b f(x)dx

When a polynomial P(x) is divided by (x-a), the remainder is P(a)

The derivative of f(x) = g(x) h(x) is given by f '(x) = g(x) h '(x) + h(x) g '(x)

The value that a function approaches as the input approaches some value