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What makes a function continuous?
A limit exists for all f(x) approaching a and the lim at f(x) = f(a)

Are all polynomial functions continuous?
Yes

What are the local min and max?
Points where f prime evaluates to zero (ie No slope bc at bottom of pit)

What is the derivative of 1  x?
1

What is the derivative of 5 + 11  6x?
6

What is the derivative of x/40?
1/40

What is the integral of 1/sqrt(x)?
2 sqrt(x)

How many feet in a mile?
5280

What is the extreme value theorem?
if a realvalued 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.

Can a function have no maximum and minimum values?
Yes, x^{3} is an example

What is Fermat's Theorem?
If f has a local max or min at c, and if f'(c) exists, then f'(c) = 0.

What is a critical number?
A number c in the domain of f such that either f'(c) = 0 or f'(c) does not exist.

Is the local min or max always a critical number?
Yes

What is the closed interval method? (to find absolute max/min)
 1. Find values of f at critical points.
 2. Find values of f at end points.
 3. Largest/smallest wins.

What is the Mean Value Theorem?
f(b)  f(a) = f'(c)(ba) At a point(s) the tangent line is parallel to the secant line.

When is a function increasing?
f'(x) > 0

When is a function decreasing?
f'(x) < 0

What is the First Derivative test?
 A. (f' + to  at c) = (f has loc max at c)
 B. (f'  to + at c) = (f has loc min at c)
 C. (f' stays the same at c) = (f does not have min/max at c)

If f' is increasing on I what does concavity look like?
Concave up :)

If f' is decreasing on I what does concavity look like?
Concave down :(

What is an inflection point?
Point where curve switches concavity

