# Thread: Tangents and Normals

1. ## Tangents and Normals

The curve y=2x^3-6x^2-2x+1 has two tangents, each of which is parallel to the line 2x+y=12. Find their equations??

2. Where is $\displaystyle y^\prime = -2~?$

3. yes based on the straight line equation

4. Originally Posted by Aniff
yes based on the straight line equation
WHAT?
Do you have any idea what this question is about?
If so, please tell us the basic facts involved.

5. sorry me bad I meant that I found y' of the straight line is -2...

6. Originally Posted by Aniff
sorry me bad I meant that I found y' of the straight line is -2...
... which means you need to find the points on the cubic curve where y' = -2

7. from what I understood the tangents have the same slope as the straight line so the derivative of the curve y=2x^3-6x^2-2x+1 which is 6x^2-12x-2=-2???
is that right??

8. Originally Posted by Aniff
from what I understood the tangents have the same slope as the straight line so the derivative of the curve y=2x^3-6x^2-2x+1 which is 6x^2-12x-2=-2???
is that right??
keep going ...

9. I'm stuck here...I'm not able to solve the equation...I'm getting weird x values

10. Originally Posted by Aniff
I'm stuck here...I'm not able to solve the equation...I'm getting weird x values
$\displaystyle 6x^2-12x-2=-2$

$\displaystyle 6x^2 - 12x = 0$

$\displaystyle 6x(x - 2) = 0$

can you solve it now?

11. sure I can...you're rock...thanks a lot