Question

Find the Points on the Lemniscate Where the Tangent Is Horizontal

A: Critical Points |
B: Inflection Points |
C: Stationary Points |
D: Saddle Points

Answer 1

To find the points on the lemniscate where the tangent is horizontal, we need to find the critical points of the lemniscate.

Step-by-step explanation:

The question asks to find the points on the lemniscate where the tangent is horizontal. To do this, we need to find the critical points of the lemniscate. A critical point occurs when the derivative of the function is equal to zero or undefined. In this case, we can find the critical points by finding the x-values that satisfy the equation:

dy/dx = 0

Once we have the x-values, we can substitute them back into the equation of the lemniscate to find the corresponding y-values. These points will be the points on the lemniscate where the tangent is horizontal.