Question

what are the absolute maximum and minimum values and inflection points of f(x) - x^3(x-2)^2, also the intervals on which the function is increasing, decreasing, concave up, down, determine the x and y intercepts and vertical and horizontal asymptotes

Answer 1

Oh, goody, calculus! College or highschool?

Answer 2

highschool

Answer 3

In response to your question, you use the first derivative to check the intervals over which the function is increasing and decreasing

Answer 4

I have the graph drawn and know that for the inflection and concaves you need the 2nd derivative but im not sure how to read it

Answer 5

uh, max and min and concavity can be done with the first derivative. second is inflection.

Answer 6

\[f'(x) = 3x^2 .... \Im \not sure how \to derive the rest o___o\]

Answer 7

got it?

Answer 8

ooooh ok

Answer 9

don't forget the product rule and the chain rule

Answer 10

(also in highschool btw)

Answer 11

I had troubles with product and chain rules, is it alright if you could explain it to me? I tried learning it how the teacher taught it but I still didnt get it

Answer 12

\[-3x^2*(x-2)^2 -x^3*2(x-2)\] is the finished derivative. I'll do it step by step now

Answer 13

product rule is f(x)=ab f'(x)=a'b+ab'

Answer 14

thank you that part helped a lot :3

Answer 15

chain rule is f(x)= a(b) f'(x)=a'(b)*b'

Answer 16

no problem, I like helping people =3

Answer 17

if you need more help, reply and I'll jump back on.

Answer 18

to find those parts, do you solve the first derivative and do the sign chart?

Answer 19

mhmm

Answer 20

thank you for helping with the chain and product rule, i get it better now