Determining slope

Question

graph is y=x^5-5x^3+4x

is the slope of the tangent line to the curve at x=a the same as the slope of the tangent line to the curve at x=-a for any other values of a? explain.

Answer 1

y is an ODD function
y' is an EVEN function
y'(a) = y'(-a).

Yes, the slope of the tangents at x=±a are identical for any value of a.