`y = 1/(x^2)` Determine the point(s) (if any) at which the graph of the function has a horizontal tangent line.
Rewrite the equation and take the derivative. Use the power rule.
`y= 1/x^2 = x^(-2)`
`y' = -2x^(-3)`
`y' = -2/x^3`
For horizontal tangent lines, the slope will always equal zero. Set the derivative function equal to zero.
Notice that if we multiplied x-cubed on both sides, we will end up eliminating the x term. This means that we will not have a solution for x.
Therefore, no horizontal tangent lines exist.