Find the absolute maximum and minimum value function fx x4

Question

1. The function is f(x, y, z) = x² y³ z⁴, compute the derivative of x.

2. Compute the derivatives of f(x, y) =ln(x²+y³).

3. Use directional derivative to approximate e^0.1√4.01 and determine the percentage error of the estimate.

4. Find the absolute maximum and minimum value function f(x) = x⁴ - 4x³ + 2x² +4x + 3 on the interval [0, 4].

5. Find the critical points for the function f(x, y) = x⁴ + y⁴ -4xy.

6. Find the maximum and minimum values of f(x, y) = 2x² +3y² subject to the constraint x² + y² = 4.

7. Find the maximum and minimum values of f(x, y, z) =xyz, subject to the constraint x² + 2y² + 3z² = 6.

8. Show the intersection of the two paraboloids f(x, y) = x² +y² and g(x, y) = 16 - x² - y² above the square -3 ?x ? 3, -3 ? y ? 3.

9. Plot the graph of the function e^-x2-y2 above the rectangle -2 ? x ? 2, -2 ? y ? 2.

Answer 1

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