Use the formula for slope of a line tangent to a parametric curve to find dy/dx for the curve c(s) = (s^-1-6s, -7s^3) at the point with s=-4

Answer 1

x = s^-1 - 6s
dx/ds = -s^-2 - 6

y = -7s^-3
dy/ds = 21s^-4

dy/dx = (dy/ds) / (dx/ds)
= (-s^-2 -6)/(21s^-4)
= (-s^-2 -6)/(21s^-4) * (s^4)/s^4)
= ( -s^2 - 6s^4)/21

when s = -4
dy/dx = (-16 - 1536)/21 = -1552/21

Answer 2

Oops. y = -7s^3
dy/ds = -21s^2

Make that fix, then follow the rest of the steps.

Answer 3

Those silly copy errors will do it every time