Find and classify the critical points of z(x, y) = x³ + 5x² + 5x + y² - 2xy.

Q: (4) Let g(x, y) = xye¬²-y². (a) Find all critical points. (b) Classify the critical points found in…

A: gx, y=xye-x2-y2⇒∇gx, y=gx, gy=ye-x2-y2-2x2ye-x2-y2,  xe-x2-y22xy2e-x2-y2⇒∇gx, y=ye-x2-y21-2x2,…

Q: 19) 1+ V3 mult. 2 A) f(x)= x* – 7x' + 8x + 4 B) f(x) = x* – 4x³ + 7x² + 8x + 4 - - 3 = x* + 4x' + 8x…

A:

Q: Find the critical point(s) of the function. f(x, y) = x' y+ 12x² – 8y + 2 (Give your answer as a…

A:

Q: Find the antiderivative of f(x) = x³ – 6x +7

A: fx=x3-6x+7 to find the antiderivative, we need to take an integration Fx=∫ fxdx

Q: Use Picard's theorem, find the largest interval for which the IVP (x – 8)(x – 1) -y'%3D (x-6)(* +1)…

A: To find the largest interval on which existence and uniqueness guarantees a unique solution. For…

Q: Let f(x,y) = 4(x + 1)²(y - 1) - y² - 8x² - 16x + 2y - 18

A: a critical point of a function is a point where the derivative is either zero or undefined. In other…

Q: Find Vf at the given point. f(x,y,z) = x³ + y² − 2z² + z ln x, - = vf|(1,2,3) i++O* (Type exact…

A:

Q: g(x) = x4 − 2x2 + 3 Find the critical numbers

A: The given function is g(x) = x4 − 2x2 + 3

Q: (3) Find all critical points of f(x,y) = -x³+3x+13-31² and classify each as yielding local max.,…

A: Critical points: (-1,0),(-1,2),(1,0),(1,2)Saddle points: (-1,0),(1,2)Relative maximum:(1,0)Relative…

Q: independent solutions of y''+ P(x)y'+ Q(x)y = 0. Assume that f1(x) has at

A:

Q: y = 0, is: %3D The general solution of y +xy +9x-4 Oa C,(3x) + C,Y,(3x) Ob C,XJ,(3x) +C,xJ_2(3x) Oc…

A:

Q: Find the critical numbers of the functions. a) f(x) = 4x° + 4x b) f(x) = x? – 4x² – 5x ) f(x) = 3x3…

A: Since you have posted a question with multiple sub-parts, we will solve first three sub-parts for…

Q: Find the critical numbers of f(x)=3x3+9x−4 and classify all local extreme values.

A: A number x=a in the domain of f is called critical number of f(x) if either f'(a)=0 or f'(x) is not…