Question

At what point is 2 the slope of curve y=x(4+x) ?

Answer 1

The point is `(-1, -3)`.

Explanation:

The slope of the curve is given by the first derivative, aka

`y = 4x + x^2-> y' = 2x + 4`

We want to solve for when `y' = 2`.

`2 = 2x + 4`

`-2 = 2x`

`x= -1`

The point is therefore `y(-1) = (-1)^2 + 4(-1) = -3 -> (-1, -3)`.

Hopefully this helps!