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Question 2: (1 point) Write the function y=x2- 8x+ 2 in the form y=a(x – 5)2...
Let ?(?)=?2−8?+4f(x)=x2−8x+4. (1 point) Let f(x) = x2 – 8x + 4. Find the critical point c of f(x) and compute f(c). The critical point c is = The value of f(c) = Compute the value of f(x) at the endpoints of the interval [0, 8]. f(0) = f(8) = Determine the min and max Minimum value = Maximum value = Find the extreme values of f(x) on [0, 1]. Minimum value = Maximum value =
(1 point) Consider the function f(x, y) = e-8x=x2-4y—y2 Find and classify all critical points of the function. If there are more blanks than critical points, leave the remaining entries blank. fx = fxx = fxy =
EXAMPLE 4 Then x2 + x-5 Let y = x3 + 6 2+x-5 y' - (x2 + x - - 5)( ++6 (x3 + 6)2 + 6 6)(2x + 1 +(x2+x - 5)( 3r? (x3 + 6) (+ 2x + 1 | ) - ( 374 +373 – 15r2 ) (x3 + 6)2 -2x3 +15x2 + 8x+4 (x3 + 5)2
Question 3 Let the function f be defined by f(x,y)--3y3 +4y2-15y +x2-8x. The set A consists of all points (x,y) in the xy-plane that satisfy 0sx S 10, 0sy s10 and x +y28.Find the global minimum value of f(x,y) over the set A. (Hint: see example 8 in lecture 7.) (6 marks) Question 3 Let the function f be defined by f(x,y)--3y3 +4y2-15y +x2-8x. The set A consists of all points (x,y) in the xy-plane that satisfy 0sx S 10,...
(1 point) The profit function for a computer company is given by P(x) = -x2 + 31x – 22 where x is the number of units produced (in thousands) and the profit is in thousand of dollars. a) Determine how many (thousands of) units must be produced to yield maximum profit. Determine the maximum profit. (thousands of) units = maximum profit = thousand dollars b) Determine how many units should be produced for a profit of at least 40 thousand....
Question Completion Status: y = -x-3 QUESTION 14 - -*-2 and goes through the point Which of the following is the equation of the line that is perpendicular to y = (-2, -3)? a. 1 13 y=g 4. b.y = C. - 8x - 19 1 11 y= x- A d.y = 8x + 13 QUESTION 15 Which ordered pair is a solution to the inequality 3x - 4y < 167 09.-3.-3) b. (4, -1)
#10 and #12 8. Find all points (.y) where fCx.y) -3x2 + 7xy -4y2 + x + y has possible relative maximum or minimum values 9. Find all points (x,y, z) where f(x,y,z) 5+ 8x 4y+x2+y2 z2has possible relativema imun or minimum value 10. Both first partial derivatives of f(x.y)-x-4xyy are zero at the points (0 11. Find all points (x,y) where f(e.y) 2x2+3xy + 5y has possible relative maximum or minimum values. Then, use the 12. Use the second...
help with these two Question 2 Let P(x) = 2x} + 7x2 – 8x +5. Use synthetic division to find the value P(10). O 5,250 O 2,625 O none of these O 2,624 2,626 Question 9 Let f(x)=x2+x, g(x)=x2-1. Find (f+g)(x). o (f+g)(x) = 0 O None of these o (+g)(x)= x+1 of+g)(x) = x4 +x3 - x2-x o(+g)(x)=2x2+x-1 X O (f+g)(x)= X-1
#3 please!! 2. Given the function f(x, y)-x2 +y -2xy -6x - 2y 5, find the following: (a) Find the critical point(s) of the function. For full credit, show all the algebra to find these and give your answer as ordered pairs. (b) Find the second order partial derivatives and use these to find the determinant of each critical point. Then classify each critical point as a saddle point, relative minimum, or relative maximum point. 3. A wine dealer sells...
Consider the function f(x) = x2 - 8x + 8. The slope of the tangent line at x = 5 is 2. Find the equation of this tangent line. (Write your answer in the form y=mx+b with no spaces - as always, if the computer marks you incorrect even if you have the answer correct but just in a different form than I use, email me and I will fix your points.) Given the function f(x)= 4x2 - 3x +...