TREE التاريخ NE 5.5 @let XX... XnX N (M, S) show that X is Eiffient Estimater. let X₁ + X₂ - - - X n N (0, 0), 070 show that the MLE of ois Fiffient Estimater and find I(0). الموضوع :
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- Suppose f(x,y)=xy(1−8x−10y).f(x,y) has 4 critical points. List them in increasing lexographic order. By that we mean that (x, y) comes before (z, w) if x<z or if x=z and y<w. Also, describe the type of critical point by typing MA if it is a local maximum, MI if it is a local minimim, and S if it is a saddle point.Suppose f(x,y)=xy(1−10x−4y). f(x,y) has 4 critical points. List them in increasing lexographic order. By that we mean that (x, y) comes before (z, w) if x<z or if x=z and y<w. Also, describe the type of critical point by typing MA if it is a local maximum, MI if it is a local minimim, and S if it is a saddle point. First point ( , ) of type Second point ( , ) of type Third point ( , ) of type Fourth point ( , ) of typeDetermine the value of x within the interval (0, 1)that minimizes the function f = (x – 1)(x – 2.5)to within ± 0.025 by the Fibonacci search method.
- Suppose f(x,y)=xy(1−1x−10y) f(x,y) has 4 critical points. List them in increasing lexographic order. By that we mean that (x, y) comes before (z, w) if x<zx<z or if x=zx=z and y<wy<w. Also, describe the type of critical point by typing MA if it is a local maximum, MI if it is a local minimim, and S if it is a saddle point. First point ( , ) of type ___Second point ( , ) of type ______-Third point ( , ) of type ________-Fourth point ( , ) of type ________Lets find out all critical points of the functionf(x, y) = xy +(2/x)+(4/y) and classify local max, local min, or saddle point2. Give an example showing that, even if f0(c) = 0, it could happen that f(x) does not have a localmaximum or minimum at x = c. How is this consistent with Fermat’s Theorem in the book?
- Find local max min and saddle points of f(x,y)= x^3-3x+3xy^2Estimate√16.2 using the linearization L(x) of f (x) =√x at a = 16. Plot f and L on the same set of axes and determine whether the estimate is too large or too small.A raptured pipe in a North Sea oil rig produces a circlar oil slick that is y meters thick at a distance x meters from the rapture. Turbulance makes it difficult to directly measure the the thickness of the slick at the source (where x=0), but for x >0, it is found that y= 0.5(x2+3x)/x3+x2+4x. Assuming the oil slick is continiously distributed, how thick would you expect it to be at the source?
- Find thearea bounded by x=y^2 and y=-x^2construct a suitable Liapunov function of the form ax2 + cy2, where a and c are to be determined. Then show that the critical point at the origin is of the indicated type. 1.dxdt=−x3+xy2,dydt=−2x2y−y3; asymptotically stable(a) False. For example, x = 0 is a critical point off (x) = x 3 but is neither a local minimum nor a local maximum.
