Minimize Pair of Objective functions (3,9), (4,1), (10,-3), (-7,11), (-8, 14), (7,-17), (6, 7), (5,8) 1) Divide them into ranks as mikobjedive function 2) Calculate crowding distance for the second rank?
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- (a) Find all critical points of the function ?(?)=?3+5?2−4?−2 . If there is more than one critical point, list them in descending order and separate them by commas. The critical point(s) is(are) = (b) Find the positive critical point of the function ?(?)=??4+4 =Find the maximum and minimum values of the function f(x,y) = 2x2 + 3y2 - 4x - 5 on the domain x2 + y2 < 64 The maximum value of f(x,y) is ? List the point(s) where the function attains its maximum as an ordered pair, such as (-6,3), or a list of ordered pairs if there is more than one point, such as (1,3), (-4,7). ? The minimum value of f(x,y) is ? List points where the function attains its minimum as an ordered pair, such as (-6,3), or a list of ordered pairs if there is more than one point, such as (1,3), (-4,7). ?maximize subject to:
- 2. Determine the definition of the piece wise linear function shown in each of the graphs 3. Consider the following sets of data points. Decide in which cases you would chose a piecewise linear model to fit the data points. 4. For any part of question 3 that was suitable for meddling with piecewise linear function: a) draw this model “by eye” b) estimate the value of y when x=12 6. Consider the set of data points in the tableTeachers get courses assigned to teach each semester. For each instructor, there are the courses that the instructor can teach based on the skill set of the instructor, and there are courses that the teacher would rather teach all the time, closer to their specialization. To be able to teach in any department, a teacher must be able to teach more than the favorite courses. Let X denote the proportion of teachers who teach the whole spectrum of courses taught in a department, and Y the proportion of teachers who teach the courses they specialize in. Let X and Y have the joint density function : f(x,y)=2(x+y),0<y<x<1 (a) Given that 10% of the teachers teach the whole spectrum of courses, what is the probability that fewer than 5% teach their favorite courses? (b) What is the expected percentage of teachers teaching their favorite courses when the proportion of teaching the whole spectrum is 0.7?Concave up (or positive concavity) over an interval means that... Group of answer choices a.as the independent quantity increases, the function over successive equally-sized intervals decreases. b.as the independent quantity increases, the function's average rates of change over successive equally-sized intervals are positive. c.as the independent quantity increases, the function over successive equally-sized intervals increases. d.as the independent quantity increases, the function's average rates of change over successive equally-sized intervals increase. e. as the independent quantity increases, the function's average rates of change over successive equally-sized intervals decrease.
- 2. Determine the intersection point of the two lines or show that they do not intersect. a) The line passing through the points (0,-9,-1) and (1,6,-3) and the line given by F(t)=(-9-4t, 10+6t, 1–2t). b. The line given by x = 1+6t, y = -1–3t, z = 4+12t and the line given by x = 4+t, y = -10-8t, z=3-5t. c. The line given by r (t)=(14+5t, -3t, 1+7t) and the line given by r(t) =(3-3t, 5+2t, -2+4t). d. Does the line passing through (-5,4,-1) and (-3,-5,0) intersect the yz-plane? If so, give the point. e. Does the line given by r (t) =(6+t, -8+14t, 4t) intersect the xz-plane? If so, give the point.The age and length of a fish have positively strong linear relation. It is observed that as a fish's age increases, its body length also increases