Question

find the slope using derivative, y=2x^4 + 3x^3 + 2x^2 - 1 where the curve crosses Ox

Answer 1

Crosses Ox?

Answer 2

yes, thats what is written in the book i can't understand it either

Answer 3

Alright, lol. Do we have any problem with the derivative part or just rhe Ox part? xD

Answer 4

the ox part. i know how to find the derivative but the Ox part is confusing me. by the way the answers are -3; 5.25 how can i get these?

Answer 5

Hmm...it's not x-intercepts or minimum or y-intercept.

Answer 6

???

Answer 7

Well, I'm trying to think of where those numbers would come from. I'm just sayign what those numbers ARENT.

Answer 8

Oh, okay, got it!. Had to use calculatorto figure out where it's getting those numbers x_x It wants to know the slope at the x-intercepts.

Answer 9

so, can you explain further? please. :)

Answer 10

Well, we need to find the x-intercepts of your graph first.

Answer 11

how?

Answer 12

Normal algebra techniques to be honest. Factoring and solving for x. Not quite sure how to factor the polynomial I assume?

Answer 13

\[X(8X^2+9X+4)\] next?

Answer 14

You factored the derivative, we need to factor the original polynomial.

Answer 15

oh,. okay.

Answer 16

Think you can do that or should we go through the process?

Answer 17

can we go through the process to check my answer?

Answer 18

Well. I'd be doing the rational roots test to see what my possible zeros could be. If we don't remember, this is where we take all the factors of the constant term and divide it by all the factors of the leading coefficient.

\[\frac{ \pm 1 }{ \pm 2,1 }\]

I know what one of the intercepts is, so we can skip the guess and check. If you remember synthetic division, we would use -1 as our starting test point. I'm guessing you remember synthetic, correct?

Answer 19

yes, i remember

Answer 20

Alright. Well if done correctly, we would get
\[(x+1)(2x ^{3}+x ^{2}+x-1)\] Which gives us one zero, but we would need to then try to factor the remaining polynomial as well. Did you already find your x-intercepts?

Answer 21

no, haha

Answer 22

Oh. Haha, well, one of them is -1 xD Would you know what to do with the remaining polynomial to get the 2nd x-intercept?

Answer 23

is it 1/2 ?

Answer 24

Yep. Good job. So now we need to find the slope at these two points. We find the slope at a point by finding the derivative and plugging in the x-coordinate of that point into the derivative. So if you take the derivative of your function and plug in -1 and (1/2), you should get your two answers.

Answer 25

i got it! haha! thank you very much :))

Answer 26

Okay, awesome ^_^