Question

http://www.webassign.net/scalcet7/4-3-006.gif
(a) On what intervals is f increasing? (Enter your answer using interval notation.)
b)On what intervals is f decreasing? (Enter your answer using interval notation.)
For a i have (2,4)
and for be I have (0,2)U(4,6) i just want to make sure its right

Answer 1

the graph is for f'(x). f(x) increases when f'(x) is positive and decreases when it's negative.

Answer 2

are my answers correct?

Answer 3

no. you gave intervals where the derivative increases/decreases

Answer 4

do you understand why your answer is wrong and how to get the correct intervals?

Answer 5

I understand why its wrong, but Im not sure how to get the right intervals

Answer 6

f will increase on intervals where the graph is positive and decrease where the graph is negative.

Answer 7

For example the graph is positive from 0 to 1, so f increases on the interval [0, 1).

Answer 8

oh okay i think i understand, um so for a it would be (3,5)?

Answer 9

and (0,1)

Answer 10

yes

Answer 11

and for b it would be (1,3) and (5,6)

Answer 12

At what values of x does f have a local maximum or minimum? (Enter your answers as a comma-separated list.) Im not really sure how to solve for this part

Answer 13

yes, although I think you should use brackets [] for the 0 and 6 because of the closed circles.

Answer 14

local maximums and minimums are where the derivative is 0, so pick out the x-intercepts of your graph

Answer 15

okay so it would be 1,3 and 5?

Answer 16

yes

Answer 17

Thank you!!

Answer 18

you're welcome