Unit 8 8.2-8.3

Question 1

What is a critical point

Answer 1

a critical point happens iff f(c) is defined and f’(c) is either 0 or undefined

Question 2

a. If f’(x) >0 then
b. If f’(x) is < 0 then
c. relative max occurs when
d. relative min occurs when

Answer 2

a. f(x) is increasing
b. f(x) is decreasing
c. f’ changes from + to -
d. f’ changes from - to +

Question 3

a. f’‘>0 means
b. f’‘<0 means
c. f’’ = 0 means

Answer 3

a. relative min
b. relative max
c. test fails

Question 4

For finding absolute/global points what do you do?

Answer 4

find y values of each critical point and end points in the domain
absolute max is largest y value, absolute min is smallest y value

Question 5

a. If f’‘(x) > 0 then f(x) is
b. If f’‘(x) < 0 then f(x) is
c. using f’ how do you know if theres an inflection point
d. using f’’ how do you know if theres an inflection point

Answer 5

a. concave up
b. concave down
c. if it changes from increasing to decreasing or decreasing to increasing there is an inflection point
d. if f’’ changes from pos to neg or neg to pos that means a point of inflection

Question 6

How to phrase things part 1!
a. f(x) is increasing on interval
(a, b)
b. f(x) is decreasing on interval
(a, b)

Answer 6

a. f(x) is increasing on the interval (a, b) because f’(x) > 0
b. f(x) is decreasing on the interval (a, b) because f’(x) < 0

Question 7

How to phrase things part 2!
a. relative min
b. relative max
c. point of inflection

Answer 7

a. f(x) has a relative min at the point x = a because f’(x) changes signs from neg to pos when x = a
b. f(x) has a relative max at the point x = a because f’(x) changes signs from pos to neg when x = a
c. f(x) has a point of inflection at the point x = a because f’‘(x) changes sign when x = a

Question 8

Stuff to Know!
a. trapezoid area
b. SA of rectangle

Answer 8

a. ((a+b)/2)h
b.2(wl+hl+hw)