# Calculus IV project

Topic:
Calculus

## Plot the original function.

Input a function, such as "f(x,y)=x^2-y^2"

## Partial derivatives.

Edit the function to be yours. Then the the curves will be drawn on the surface above x=2 and y=3 on the surface itself. Write a short description of how this plot is related to , , , and . Include the sign of each of these, and how it is visible in the plot.

## Contour map (2d)

Edit the function to build a contour map of the function. Write a short description of what this plot is demonstrating. Be as thorough as possible: relate the plot to the function value as well as derivatives. What does the contour map represent? How is it computed? And what is it useful for?

## Tangent plane

Edit the function, and edit the fx, fy (partial derivative vectors) so that the last components are the fx(a,b) and fy(a,b). Then move around the point (a,b) to alter the base point for the tangent plane. What does the tangent plane represent? How is it computed? And what is it useful for?

## Exploration.

Have fun! Make another plot that demonstrates something related to our class. Ensure that you write a description about what concept you are demonstrating, and how explicitly the plot is constructed to demonstrate this concept.

## Text responses for the plots above.

Give your responses to the prompts in this space.