Question

At what value(s) of x does f have a local maximum?
At what value(s) of x does f have a local minimum? http://www.webassign.net/scalc/4-3-6.gif

Answer 1

Local maxima and minima occur at "bumps" in the graph (or like the crests and troughs of a wave). Look at the graph - at which x values does the graph look like it has a bump?

Answer 2

1,3,5,7,8 @OakTree

Answer 3

Sounds good to me. Now, should a minimum be a "crest" or a "trough"?

Answer 4

minimum= 1,5,8
max=3,7,9

Answer 5

@OakTree

Answer 6

That's right.

Answer 7

there is no local max at x = 9. That is the absolute maximum (on the interval [0,9])

Answer 8

Oh, jim is right. I didn't notice that 9 in there.

Answer 9

oh but when i submitted it it said i got the max wrong when i put 3&7

Answer 10

oh wait, this is f ' (x)

they want local mins and maxes for f(x)

Answer 11

yes

Answer 12

look at the roots of f ' (x)

use the first derivative test

Answer 13

are the roots 2,4,6

Answer 14

yes

Answer 15

use the first derivative test

Answer 16

on what?

Answer 17

to determine where the local mins and maxes are

Answer 18

use f ' (x) to determine where the local mins and maxes are on f(x)

Answer 19

https://www.math.hmc.edu/calculus/tutorials/extrema/

Answer 20

but there is no equation given

Answer 21

you can use the graph

Answer 22

the points on f ' (x) that are above the x axis correspond to regions where f ' (x) > 0