find the point(s) on the graph of y = (2x4 + 1)(x - 5) where the tangent line slope is 1.

Answer 1

I assume you meant
y = (2x^4 + 1)(x - 5)

using the product rule

dy/dx = (2x^4+1)(1) + 8x^3(x-5)
simplify and set it equal to 1 gives me
2x^4 + 1 + 8x^4 - 40x^3 = 1
10x^4 - 40x^3 = 0
10x^3(x-4) = 0
so x = 0 or x = 4

those are the x's of your two points where the slope of the tangent is 1
sub into the origianal to get the y's