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3 pages/β825 words
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Style:
APA
Subject:
Mathematics & Economics
Type:
Math Problem
Language:
English (U.S.)
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Topic:
Mathlab Coding and Finding the Directional Derivative of the Function
Math Problem Instructions:
Hello, please solve the math problems on the document. Please show all your calculations on paper. This homework requires some level of Matlab coding.
If MATLAB coding is too complicated and no writers know how to code it, they can disregard it and solve the questions numerically.
Math Problem Sample Content Preview:
PROBLEM C2
Solution
The function is, f (x, y) = x2-xy
At (x, y) = (2, -3) in the direction of vector v= (35, 45)
First, you find the function's gradient and evaluate it at the specified point.
You differentiate the function with respect to each variable to determine the gradient of the function, which is a vector.
∇f (x, y) =( ∂f∂x, ∂f∂y)
∂f∂x = 2x – y , ∂f∂y = -x
The gradient at point (2, -3) is;
∇ (x2-xy) (x, y) = (2x-y, -x)
Substitute x = 2 and y = -3 in the equations for ∂f∂x and ∂f∂y,
that is ∂f∂x = 2x – y = 2(2) – (-3) = 7 and ∂f∂y = -x = -(2) = -2
= (7, -2)
Length of the vector Ε« =352+452=1 Since the length of the vector is 1 then it’s already normalized.
Finally, the directional derivative is the dot product of the gradient and the normalized vector. This is, D= (7, -2). ( 35, 45)
=135
PROBLEM C3
* The function is, f (x, y) = x2 - xy +3y2
You differentiate the function with respect to each variable to determine the gradient of the function, which is a vector.
∇f (x, y) =( ∂f∂x, ∂f∂y)
∂f∂x = 2x – y , ∂f∂y = -x + 6y
The gradient = (2x-y, -x + 6y)
* f (x, y...
Solution
The function is, f (x, y) = x2-xy
At (x, y) = (2, -3) in the direction of vector v= (35, 45)
First, you find the function's gradient and evaluate it at the specified point.
You differentiate the function with respect to each variable to determine the gradient of the function, which is a vector.
∇f (x, y) =( ∂f∂x, ∂f∂y)
∂f∂x = 2x – y , ∂f∂y = -x
The gradient at point (2, -3) is;
∇ (x2-xy) (x, y) = (2x-y, -x)
Substitute x = 2 and y = -3 in the equations for ∂f∂x and ∂f∂y,
that is ∂f∂x = 2x – y = 2(2) – (-3) = 7 and ∂f∂y = -x = -(2) = -2
= (7, -2)
Length of the vector Ε« =352+452=1 Since the length of the vector is 1 then it’s already normalized.
Finally, the directional derivative is the dot product of the gradient and the normalized vector. This is, D= (7, -2). ( 35, 45)
=135
PROBLEM C3
* The function is, f (x, y) = x2 - xy +3y2
You differentiate the function with respect to each variable to determine the gradient of the function, which is a vector.
∇f (x, y) =( ∂f∂x, ∂f∂y)
∂f∂x = 2x – y , ∂f∂y = -x + 6y
The gradient = (2x-y, -x + 6y)
* f (x, y...
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