Question

In: Math

ƒ(x,y)= x3 + 3xy2 - 15x + y3 - 15y For this question i need to...

ƒ(x,y)= x3 + 3xy2 - 15x + y3 - 15y

For this question i need to calculate the critical points and all local minima, local maxima and saddle points. How should this be done?

Solutions

Expert Solution

I used the basic rule of derivative and remember the partial derivative rule, when use differentiate with respect to x, then y will consider as constant ; and when we differentiate w.r to . y then x will consider as constant. Thank you


Related Solutions

Let f(x,y) = 3x3 + 3x2 y − y3 − 15x. a) Find and classify the...
Let f(x,y) = 3x3 + 3x2 y − y3 − 15x. a) Find and classify the critical points of f. Use any method taught during the course (the second-derivative test or completing the square). b) One of the critical points is (a,b) = (1,1). Write down the second-degree Taylor approximation of f about this point and motivate, both with computations and with words, how one can see from this approximation what kind of critical point (1,1) is. Use completing the...
Let f(x,y) = 3x3 + 3x2 y − y3 − 15x. a) Find and classify the...
Let f(x,y) = 3x3 + 3x2 y − y3 − 15x. a) Find and classify the critical points of f. Use any method taught during the course (the second-derivative test or completing the square). b) One of the critical points is (a,b) = (1,1). Write down the second-degree Taylor approximation of f about this point and motivate, both with computations and with words, how one can see from this approximation what kind of critical point (1,1) is. Use completing the...
Let x,y ∈ R3 such that x = (x1,x2,x3) and y = (y1,y2,y3) determine if <x,y>=...
Let x,y ∈ R3 such that x = (x1,x2,x3) and y = (y1,y2,y3) determine if <x,y>= x1y1+2x2y2+3x3y3    is an inner product
Let f (x, y) = -x3 - y3 + 9xy - 26. Check that (0,0) and...
Let f (x, y) = -x3 - y3 + 9xy - 26. Check that (0,0) and (3,3) are stationary points of f and classify these points as maximum, minimum or saddle point. Obtain the maximum or minimum value of f.
1.Consider the function: f(x, y) = 2020 + y3-3xy + x3. a) Find fx(x, y), and...
1.Consider the function: f(x, y) = 2020 + y3-3xy + x3. a) Find fx(x, y), and fye(x, y). b) Find all critical points of f(x, y). c) Classify the critical points of f(x, y) (as local max, local min, saddle). 2.Consider f(x) = 2x-x2and g(x) = x2 a) [2 points] Find the intersection points (if any) of the graphs of f(x) and g(x). b) [4 points] Graph the functions f(x) and g(x), and shade the region bounded by: f(x), g(x),...
For this problem, consider the function f(x) = x3 - 9x2 +15x + 3.
  For this problem, consider the function f(x) = x3 - 9x2 +15x + 3. A. Determine the intervals on which f(x) is increasing and intervals on which f(x) is decreasing. B. Determine all relative (local) extrema of f(x). C. Determine intervals on which f(x) is concave up and intervals on which f(x) is concave down. D. Determine all inflection points of f(x).
Consider the following. y = −x3 + 6x2 + 15x − 9 Give the relative extrema...
Consider the following. y = −x3 + 6x2 + 15x − 9 Give the relative extrema and points of inflection. (If an answer does not exist, enter DNE.)
y''' - 7y'' + 15y' - 9y = 8e^(x) - 9x A) Find the fundamental set...
y''' - 7y'' + 15y' - 9y = 8e^(x) - 9x A) Find the fundamental set of solutions of the reduced equation. (Hint: 3 is a root of the characteristic polynomial.) B) Find a particular solution of the given equation. C) Find the general solution of the given equation.
Let P(x,y) = -15x^2 -2y^2 + 10xy + 10x +8y + 11 where P(x,y) is the...
Let P(x,y) = -15x^2 -2y^2 + 10xy + 10x +8y + 11 where P(x,y) is the profit in dollars when x hundred unit of item A and y hundred units of item B are produced and sold. A.Find how many items of each type should be produced to maximize profit? B.Use the Second Derivates Test for local extrema to show that this number of items A and B results in a maximum?
(1) z=ln(x^2+y^2), y=e^x. find ∂z/∂x and dz/dx. (2) f(x1, x2, x3) = x1^2*x2+3sqrt(x3), x1 = sqrt(x3),...
(1) z=ln(x^2+y^2), y=e^x. find ∂z/∂x and dz/dx. (2) f(x1, x2, x3) = x1^2*x2+3sqrt(x3), x1 = sqrt(x3), x2 = lnx3. find ∂f/∂x3, and df/dx3.
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT