3D Practice Problems

Here are some functions that you can use to practice the techniques you've learned so far. Try graphing them yourself first, then check your answer.

1. f(x,y) = x3 - 3xy2

Click here for a hint.

Click here to check your answer to problem 1.

2. f(x,y) = 2xy(x2 - y)(x2 + y)

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Click here to check your answer to problem 2.

3. f(x,y) = (1 - x2 - y2)x

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Click here to check your answer to problem 3.

4. f(x,y) = (1 - x2 - y2)xy

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Click here to check your answer to problem 4.

5. Revolving a 2D graph around one of the three axes yields a surface of revolution. Graph the surface of revolution formed by revolving the circle (x - 3)2 + y2 = 1 around the z-axis.

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Click here to check your answer to problem 5.

6. f(r,t) = r2cos(4t)

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Click here to check your answer to problem 6.

7. f(r,t) = sin(cr), c = 2pi

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Click here to check your answer to problem 7.