Answer
$(-2,-5)$
Work Step by Step
Given that $f(x)=x^2+4x-1$, the function will have a horizontal tangent when the derivative is equal to 0, since the slope will indicate that there is no change in the y value of the tangent when x changes.
$f'(x)$ is found using the power rules:
$f'(x)=2x+4$
We let $f'(x)$ be equal to zero.
$2x+4=0$
$x=-2$
$f(-2)=-5$
Thus, at the point $(-2,-5)$, there is maximum or a minimum where the graph will have a horizontal tangent.
