Determine the points in which the given function has a horizontal tangent line. y = x^(3) + x

Question

Determine the points in which the given function has a horizontal tangent line.

y =
`x^(3) + x`

Answer 1

`\bf y=x^3+x\implies \cfrac{dy}{dx}=3x^2+1 \\\\ \textit{now setting the derivative to 0} \\\\ 0=3x^2+1\implies \cfrac{-1}{3}=x^2\implies \sqrt{\cfrac{-1}{3}}=x \\\\\\ \cfrac{√(3)}{3}\ i=x`

meaning, it doesn't have one :)