For a $\mathcal{C}^1-smooth$ bump function $b: \mathbb{R}^2 \rightarrow \mathbb{R}$ we show that the gradient range $\nabla b(\mathbb{R}^2)$ is the closure of its ...

As a tangent is a straight line it is described by an equation in the form \(y - b = m(x - a)\). You need both a point and the gradient to find its equation. You are usually given the point - it's ...

To construct the tangent to a curve at a certain point A, you draw a line that follows the general direction of the curve at that point. An example of this can be seen below. Once the tangent is found ...