Thread: 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)

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)

So we have that
so then we would have
Can you see what to do from there?

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

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

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...