Question

How do you determine equations for the tangents to the points on the curve `y=-x^4+8x^2` such that the tangent lines are perpendicular to the line x=1?

Answer 1

`y=0 ^^ y=16`

Explanation:

If the tangent lines are perpendicular to `x=1` they are parallel to x-axis. Slope of the x-axis is equal to zero and every line parallel with x-axis has the same slope, so `k=0`.

`k=y'=-4x^3+16x=0`
`-4x(x^2-4)=0 <=> x=0 vv x^2-4=0`
`x=0 vv x=-2 vv x=+2`

`y(0)=0 => y=0`
`y(-2)=16 => y=16`
`y(+2)=16 => y=16`

So, tangents are: `y=0 ^^ y=16`

Video Lesson on this problem