SOLUTION: Find k and the points of contact if the parabola y = x^2 − k touches the quartic y = x^4 at two points.

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Question 1143840: Find k and the points of contact if the parabola y = x^2 − k touches the quartic y = x^4 at two points.
Found 2 solutions by Alan3354, ikleyn:
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
Find k and the points of contact if the parabola y = x^2 − k touches the quartic y = x^4 at two points.
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The 2 curves are tangent for k = 0.25
They intersect for any value of k < 0.25
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If you mean tangent, you should say that.
They "touch" at the intersections of k < 0.25, an infinite # of points.

Answer by ikleyn(52834) About Me  (Show Source):
You can put this solution on YOUR website!
.

The figure at k = 0.25



    graph%28+330%2C+330%2C+-3%2C+3%2C+-2%2C+3%2C%0D%0A++++++++++x%5E2-0.25%2C+x%5E4%0D%0A%29

    Plots y = x%5E2-0.25 (red)  and  y = x%5E4 (green).



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