xQx + bx where Q = (a/2 9/2) and Problem Classify the stationary points of f: R2 → R, f(x) = b=(1,2) for a E R. Consider all possibilities depending on a.
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- Find the constant of proportionality. y is directly proportional to x. If x=30, then y=15.Find y as a function of a if y(1) = 2, y(1) = 1. y = r²y" + 7ry +9y = 2³,Consider the function f(x, y) = 2x² + xy² − 6xy + 5x + 2. (a) Show that (1,3) is a stationary point of f. (b) Classify the stationary point (1, 3).
- Find and classify all stationary points of the function f(x,y) = x³ + xy + y² − x.Consider the function: f (x, y) = 2x2 + xy2 - 6xy + 5x + 2 1. Show that (1,3) is a stationary point of f. 2. Classify the stationary point (1,3).Suppose that f(x, y) = -2z4+3 zy2 + 3y2, z=rcos (t) and y=rsin(t). Find af af and (write your answers as functions of the pair r and t). Ot Or af Or af ICH
- 2. Consider the function f: R²R such that f(x, y) = x²y-2xy² +6xy-3y² +18y +4. (a) Show that f has precisely two stationary points: (-4,-1), and (0,3). (b) Determine the nature of these two stationary points.consider a function f, defined by f(x,y) = -y/√x2+y2 what is the behavior of f along the line y=x when x>o; that is, what is the value of f(x,x) when x>0? If we approach (0,0) by moving along the line y=x in the first quadrant(thus considering f(x,x) as x→0+, what value do we find for the limit?