Test 3

Question 1

Extreme Value Theorem

Answer 1

Requires continuity, no undefined values

Question 2

How to find max/min

Answer 2

Find critical numbers by setting derivative to zero, find f(x) at endpoints as well as critical numbers by plugging into og function, the bigger one is big max, smaller one is small min

Question 3

Rolle’s theorem

Answer 3

must be continuous, differentiable, and f(a) = f(b)

Question 4

How to do the main value theorem

Answer 4

Find the equation f’(c) = f(b) - f(a) / b - a, set x values to c to find c

Question 5

How to find increasing/decreasing

Answer 5

Find critical numbers of derivative, make number like according to those values

Question 6

The first derivative test

Answer 6

If derivative changes from positive to negative at c, then the C is its local maximum. If derivative changes from negative to positive at c, the C is its local minimum.

Question 7

Concave up

Answer 7

Right halfway uppy cuppy, increasing f’>0, decrease f’<0

Question 8

Inflection point

Answer 8

If f is continuous there and the concavity of the curve changes at P

Question 9

The indeterminate forms

Answer 9

0/0, infinity/infinity, 0(infinity), 0^0, 1^infinity, infinity - infinity

Question 10

For using l’hospital’s rule

Answer 10

Find the IDF, label it, find derivative and figure out limit

Question 11

List of curve sketching

Answer 11

1. Find Domain
2. Find intercept, for x solve f(x) = 0, for y solve f(0)
3. Asymptotes, vertical set denominator to zero, oblique long division
4. Increase/decrease
5. Local extrema
6. Concavity and inflection points

Question 12

Antiderivatives

Answer 12

F(x) = 1/n +1 x^n + 1 + C

Question 13

Newton’s method

Answer 13

X2 = x1 - f(x1)/f’(x1)