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Let [tex]a[/tex] be a constant, and let [tex]f(x)=13x^4-19a^2x^2+20a^3x-23[/tex]. Show that there are exactly two points on the curve [tex]y=f(x)[/tex] that have a common tangent line.

So far my strategy has been to find the first and second derivatives, as hopefully seeing where the first derivative crosses the x-axis or something like that will help, but I am not sure where to go from there.

Sagot :

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