Min, max and saddle points
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1) Find the local maximum and minimum values and saddle point(s). Here is the function:
f(x,y) = x^3y + 12x^2 -8y
2) Use Lagrange multiplier to find the extreme values (i.e. the max and min) of:
f(x,y) = 4x+6y
subjected to the constraint
x^2 + y^2 = 13
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Solution Summary
This solution shows the steps for determining the minimum value, maximum value, and saddle points for the given function. Additionally, this solution shows how to use the Lagrange multiplier to find the extreme values of a given function.
Solution Preview
1)
first we calculate the gradient and set them to zero
df/dx = 3(x^2)y + 24x = 0
df/dy = x^3 - 8 =0
this leads to one solution x = 2, y = -4.
Next, we use the second ...
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