Question

At what point is the tangent to f(x)= x^2+4x- 1 horizontal?

Answer 1

The tangent is horizontal when the tangent line's slope is 0. The tangent line's slope at any point should be the slope of f(x) at that same point. So you need to find the slope of f(x), which will be an expression of x. When that expression is 0, that's the point where the tangent is horizontal