Consider the function F (2,y) = x y2 + x y – 6 y? – 6 z – 6 y + 38 . (a) Find the critical points, where Fr (x,y) = Fy (x,y) = 0. Enter the coordinates of the critical point with the greater y-value. Enter in the form (x,y). Frz Fry (b) Enter the matrix at that point. Fyz Fyy. To enter the matrix click on the 3 x 3 grid of squares below and replace the entries with your answer. sin (a) f 00

If two functions y1(t), Y2(t) E C*(R are linearly independent, then y (t) and y2(t) must also be linearly independent. true false

Which of the following functions V(y1, y2) is a Lyapunov function for the dynamical system y₁ = (4-₁)ex, y2 = y²-y²y₂ Select one: a. V(v₁.32) = -4+(2-1)³ b. V(v₁.y2) = -²³ +²² c. V(v₁.92) = ₁ + y/² C. Od. V(y₁, y2) = (y₁ - 4)4+ (y2 - 1)²

The function of two variables ƒ(x, y) = 3x² – 2xy − 10x + y² + 2y +9 has a stationary point at (2, 1). At this stationary point, the Hessian matrix for fis H=[6₂ -2 Select the option that describes this stationary point. Select one: 2]. -2 The stationary point is a saddle point. The nature of the stationary point cannot be determined from the Hessian matrix. The stationary point is a local maximum. The stationary point is a local minimum.