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## Homework Statement

Show that the tangent to the curve [tex]y=(x^2+x-2)^2+3[/tex] at the point where x =1 is also tangent to the curve at another point.

## Homework Equations

[tex]y=(x^2+x-2)^2+3[/tex]

## The Attempt at a Solution

[tex]y'=2(x^2+x-2)(2x+1)[/tex]

[tex]y'(1)=0[/tex]

[tex]0=2(2x+1)(x+2)(x-1)[/tex]

x= -1/2, -2, 1

Would this be correct?

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