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