Exam 3

Question 1

Extreme Value Thm

Answer 1

If f is continuous on a closed interval [a,b], then f attains an abs. max and an abs. min values in [a,b]

Question 2

Fermat’s Thm

Answer 2

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

Question 3

Rolle’s Thm

Answer 3

let f be a function that satisfies the following:
1. f is a continuous on [a,b]
2. f is differentiable on (a,b)
3. f(a) = f(b)
Then there is a number c in (a,b) such that f’(c) = 0

Question 4

MVT

Answer 4

let f be a function that satisfies the following
1. f is continuous on [a,b]
2. f is differentiable on (a,b)
Then there is a c in (a,b) such that f’(c) = f(b)-f(a) / b-a or f’(c) (b-a) = f(b) - f(a)

Question 5

f’(x) < 0
f’‘(x) > 0

Answer 5

f’ decr.
f’’ cc up
(

Question 6

f’(x) > 0
f’‘(x) >0

Answer 6

f’ incr.
f’’ cc up
)

Question 7

f’(x) > 0
f’‘(x) < 0

Answer 7

f’(x) incr.
f’‘(x) cc down
(

Question 8

f’(x) < 0
f’‘(x) < 0

Answer 8

f’ decr.
f’’ cc down
)