Use the following visual to explore the gradient. Remember that the gradient points in the direction of steepest ascent. The gradient is shown on the contour plot in green. The opposite direction of t...Use the following visual to explore the gradient. Remember that the gradient points in the direction of steepest ascent. The gradient is shown on the contour plot in green. The opposite direction of the gradient (in orange) is the direction of steepest descent. Move the point A around in the 3D view and observe how the gradient is always orthogonal to the level curve. Move the slider m to see different level curves f=m. Do the gradients get longer or shorter?
Use the following visual to explore how a contour plot can be used to gain information about the partial derivatives. The arrows in the x- resp. y-direction show you the direction in which you...Use the following visual to explore how a contour plot can be used to gain information about the partial derivatives. The arrows in the x- resp. y-direction show you the direction in which you are looking when you want to examine the partial with respect to x- resp. y. The length of the arrows indicates the value of the partials in those directions. Also, if the arrow points in the direction of the negative axis, that means that the partial derivative is negative.
