4.1-4.4.txt

A limit exists for all f(x) approaching a and the lim at f(x) = f(a)

Yes

Points where f prime evaluates to zero (ie No slope bc at bottom of pit)

-1

-6

1/40

2 sqrt(x)

5280

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.

Yes, x³ is an example

If f has a local max or min at c, and if f'(c) exists, then f'(c) = 0.

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

Yes

• 1. Find values of f at critical points.
• 2. Find values of f at end points.
• 3. Largest/smallest wins.

f(b) - f(a) = f'(c)(b-a) At a point(s) the tangent line is parallel to the secant line.

f'(x) > 0

f'(x) < 0

• 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)

Concave up :)

Concave down :(

Point where curve switches concavity