If f(x, y) = xy, find the gradient vector Vf(3, 7) and use it to find the tangent line to the level curve f(x, y) = 21 at the point (3,7). gradient vector tangent line equation × Sketch the level curve, the tangent line, and the gradient vector. 14 12 10 8 6 4 2 y 5 10 15 20 X y 15 10 5 -5 5 10 15 20 20

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Find the directions of maximum and minimum change of f at the given point, and the values of the maximum and minimum rates of change. fx, y) = 4ye*, (5, 2)

Determine the values of p. q, and r so that the function f(z) = pr + qa + rz will have an inflection point at (1,2) and the slope of the tangent line at (1,2) will be-2. %3D item 5 pdf

Ohm's law states that the voltage drop Vacross an ideal resistor is linearly proportional to the current i flowing through the resistor as V= iR. Where R is the resistance. However, real resistors may not always obey Ohm's law. Suppose that you perform some very precise experiments to measure the voltage drop and the corresponding current for a resistor. The following results suggest a curvilinear relationship rather than the straight line represented by Ohm's law. i -1 - 0.5 - 0.25 0.25 0.5 1 V -637 -96.5 -20.25 20.5 96.5 637 Instead of the typical linear regression method for analyzing such experimental data, fit a curve to the data to quantify the relationship. Compute V for i = 0.1 using Polynomial Interpolation.

Ohm's law states that the voltage drop Vacross an ideal resistor is linearly proportional to the current i flowing through the resistor as V= iR. Where R is the resistance. However, real resistors may not always obey Ohm's law. Suppose that you perform some very precise experiments to measure the voltage drop and the corresponding current for a resistor. The following results suggest a curvilinear relationship rather than the straight line represented by Ohm's law. i -1 - 0.5 - 0.25 0.25 0.5 1 V -637 -96.5 -20.25 20.5 96.5 637 Instead of the typical linear regression method for analyzing such experimental data, fit a curve to the data to quantify the relationship. Compute V for i = 0.1 using Newton's Divided Difference Method.

Determine the values of p, q, and r so that the function f(x) = px° + qx² + rx will have an inflection point at (1, 2) and the slope of the tangent line at (1,2) will be -2.

Take the derivative