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)   (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)   (Show Source): You can put this solution on YOUR website!
.

The figure at k = 0.25



    

    Plots y =  (red)  and  y =  (green).



"It is better one time to see than 100 times to hear" (a proverb).


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