### Local maximum and minimum and saddle points

Find the local maximum and minimum values and the saddle points of the functions. 1.)f(x,y)= xy(1-x-y) 2.)f(x,y)= (x^2y^2 - 8x + y)/(xy)

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Find the local maximum and minimum values and the saddle points of the functions. 1.)f(x,y)= xy(1-x-y) 2.)f(x,y)= (x^2y^2 - 8x + y)/(xy)

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An object moves along the x-axis with initial position x(0)=2. The velocity of the object at time t is greater than or equal to 0 is given by v(t)=sin((pi/3)t). a.) What is the acceleration of the object at time t=4? b.) Consider the following two statements. Statement I: For 3<t<4.5, the velocity of the object is increa

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Consider the following problem for u = u(x,t): , , a) Seeking a solution of this problem of the form , show that f and g satisfy the coupled system ; where and ; , ; , . b) Eliminating g between the differential equations in a), show that f satis

Please follow all instructions and answer accordingly. See the attached file. Consider a projectile of mass m

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Suppose that p and q are continuous on some open interval I, and suppose that y1 and y2 are solutions of the ODE y'' + p(t)y' + q(t)y = 0 on I. (a) Suppose that y1, y2 is a fundamental set of solutions. Prove that z1, z2, given by z1 = y1 + y2, z2 = y1 − y2, is also a fundamental set of solutions. (b) Prove that i

Solve Laplace of u = 0 subject to the conditions: u(x,0) = f1(x) u(0,y) = 0 u(x,b) = 0 u(a,y) = 0 0<x<a 0<y<b (The question attachment contains a slightly different question. The question is restated correctly in the solution attachment)