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)

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- Apr 27th 2008, 06:45 PMfinch41Tangent 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) - Apr 27th 2008, 06:51 PMMathstud28
- Apr 28th 2008, 03:43 AMfinch41
i think i did that but i cannot figure out what to do with it... since it will have two variables x and x1

- Apr 28th 2008, 01:09 PMfinch41
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 - Apr 28th 2008, 01:40 PMfinch41solved... 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...