# Math Help - Tangent to the curve

1. ## Tangent to the curve

Here's the question:

There are two points on the curve y = x^4 - 2x^2 - x that have a common tangent line. Find those points.

I'm stuck.

(ps. sorry for double post but the previous one had a poor title)

2. Originally Posted by finch41
Here's the question:

There are two points on the curve y = x^4 - 2x^2 - x that have a common tangent line. Find those points.

I'm stuck.

(ps. sorry for double post but the previous one had a poor title)
$f'(x)=4x^3-4x-1$

So we have that $y-f(x_0)=f'(x_0)(x-x_0)$
so then we would have $y-(x_0^4-2(x_0)^2-x_0)=(4x_0^3-4x_0-1)(x-x_0)$
Can you see what to do from there?

3. i think i did that but i cannot figure out what to do with it... since it will have two variables x and x1

4. so like no one can do this?

i gave it to my math teacher today and he tried some stuff and dediced best to take it home and look at it later

5. ## solved... or is it?

well see i got the answer
i decided i would sketch the curve accurately so i found all the important points and then estimated the common tangent

and along the process i found that f prime of 1 and f prime of -1 are both -1
and when i finished sketching the curve i estimated the common tangent line at about those points

and when i found the equation of the tangent line at each point they turn up the same equation

but is this luck?

is there a more methodical approach?

hmm...