y=(x^3+2x)^4 at x=-1

Question

Find the tangent line

Answer 1

When x=-1, y=(-1-2)⁴=81, so the tangent line must pass through (-1,81).

dy/dx=4(x³+2x)³(3x²+2)=4(-1-2)³(3+2)=-540, the slope of the tangent.

So y-81=-540(x+1) in slope-intercept form, y=-540x-540+81=-540x-459.

The general form is 540x+y+459=0.