The gradient vector

• A gradient vector is a vector that is used to describe the direction and magnitude of a uniform change in a scalar quantity (e.g. temperature, pressure, or density). The gradient of a function at a point is the directional derivative of that function in the neighborhood of that point.

Let’s summarize what we learned. We found an equation that allows us to find the normal vector of a level curve at any point on the curve. The negative 4, 2 were the coefficients of the x and y in the linear approximation. Moreover, the coefficients of the delta x and X delta y were the same. So the equations were just x derivatives and y derivatives. So. if I take the derivative of fat a point (vector, x derivative, y derivative), the vector formed by that derivative is perpendicular to the level curves at that point. The vector (F_x(x_0, y_0), F_y(x_0,y_0)) The vector (f sub x, f sub y) is called the gradient of f. We’ll study it next (F_x,F_y)