Question

Differentiate x(x-4)^3

Answer 1

its a tricky one, but here is what i get

Answer 2

use product rule
\[\Large \frac{d}{dx}(x)(x-4)^3+\frac{d}{dx}((x-4)^3) *x\]

Answer 3

\[x(3(x-4)^2+(x-4)^3\]

Answer 4

it should be

\[\Large x(3(x-4)^2)+(x-4)^3\]

Answer 5

could i simplify that by factoring out an x-4^2

Answer 6

yes you can if you want .

Answer 7

im trying to do some analysis for a graph, finding the increase and decrease

Answer 8

these kinds of derivatives are killing me

Answer 9

is this legal?

Answer 10

\[(x-4)^2(4x-4)\]

Answer 11

\[(x-4)^2(3x+(x-4))\]
You factored the x-4's out like this?
Then simplified?
Yes very nice :) will make it a bit easier to find your critical points.

Answer 12

ZEP!!

Answer 13

lol, calle! :o

Answer 14

Grr I miss calc 1, you get to do all this fun math! :)
Everyone else on here is doing boring algebra and geometry T.T

Answer 15

so my roots should be 1,4

Answer 16

or crit points

Answer 17

cool beans :O set up that table lady!

Answer 18

oh woops, i think your other CP should've been 2 shouldn't it? due to the square.
Or rather, +/-2? :o

Answer 19

nevermind XD silly zep..

Answer 20

weird

Answer 21

Oh oh oh, it's a cubic function :)
Lemme give a quick example of how that can happen

Answer 22

hmm the book says only 1 is a root

Answer 23

or a crit point