Question

Use the first derivative to determine where the function

F(x)= 48x^3-1512x^2+15840x+8

is increasing and decreasing.

Use interval notation.

Can you please explain on how you got the answer as well? I didnt pay attention to class enough :(

Answer 1

did you find the derivative?

Answer 2

let me know when you find the derivative and we'll go over the rest.

Answer 3

144x^2-3024x+15840 here ty

Answer 4

ok divide through by 144

Answer 5

you'll get an easily factorable expression

Answer 6

one you've found the roots, look at the intervals between and outside the roots, look at whether f'(x) is positive or negative in those intervals. If f'(x) is positive in an interval f(x) is increasing on that interval, If f'(x) is negative in an interval f(x) is decreasing on that interval

Answer 7

all good on this or do you have questions?

Answer 8

1 21 110 these are the roots

Answer 9

but
Im not getting what are you are saying about the intervals

Answer 10

Im sorry for not being smart :/

Answer 11

factor f'(x) and find the roots

Answer 12

hint:

it looks like this

Answer 13

then ask yourself where it is positive and where it's negative.

Answer 14

the roots from the factors?

Answer 15

yep

Answer 16

144x^2-3024x+15840 this is f'(x) this is x^2-21+110 with 144 factored out

Answer 17

yep

Answer 18

so Im taking square rootsof the first or second?

Answer 19

it's a quadratic, find the roots, by using the quadratic formula
*OR* by factoring it (which is pretty easy in this case, so, do that)

Answer 20

ah now I know what you mean, (x-11)(x-10) so its x=10 x=11

Answer 21

perfect.

Answer 22

now... where is f'(x) negative? (use my rough sketch, now that you know the roots are 10 and 11)

Answer 23

never?