Find all locations and values of the local maxima and minima and the location of

Question

Find all locations and values of the local maxima and minima and the location of the saddle points of the given function fxy)-x3y3+9x2-92-4 Select the correct choice below and fill in any answer boxes within your choice. O A. There are local maxima located at 0 B. There are no local maxima. Select the correct choice below and fill in any answer boxes within your choice. O A. The values of the local maxima are O B. There are no local maxima. Select the correct choice below and fill in any answer boxes within your choice. 0 A. There are local minima located at 0 B. There are no local minima. (Simplity your answer. Type an ordered pair. Use a comma to separate answers as needed.) (Simplify your answer. Use a comma to separate answers as needed.) (Simplify your answer. Type an ordered pair. Use a comma to separate answers as needed.)

Explanation / Answer

f(x,y) =x^3+y^3 +9x²-9y²-4

Find partial derivative as

fx= 3x² +18x =3x(x+6)

fy= 3y² -18y =3y(y-6)

To find critical point, solve fx=0 and fy=0

3x(x+6) =0

x = -6, 0

Now

3y(y-6) =0

y= 0, 6

hence critical points are (-6, 6),(-6,0)(0, 6) and (0,0)

-----------------

Local maxima located at (-6,0)

The value of local maxima are 104

---------------

Local minima located at (0,6)

The value of local minima are -112

-------------

Saddle point located at (-6,6), (0,0)

The value of Saddle point  are -4

Related Questions

Navigate

• Browse (All)
• Browse F
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.