find the values of x where the tangent lines y=x^8 and y=x^9 are parallel

Answer 1

The tangent lines will be parallel when the derivatives are equal, i.e.

8x⁷ = 9x⁸

That means at the origin the curves will be horizontal ( i.e. at the vertices) and

when 8=9x, i.e. at x=8/9.