Did I do this one correctly? I only found one critical point and just wanted to double check that I was correct. Thanks! 2.xy t By- Sx-Ay +2.St (2-)2 =hX t 6/28+5) -4=0-260= えてl0. Find and Classify all critical points of f(x,y)=-R +-2x + 4-5=0リ= 2x +5こ13.ty=x+b4=4=D013.a saddle point%3Dニ-2.6-1CRITICAL POIN T: (-2,1) This is

Let us consider two variable function z=f(x,y) To find the maxima and minima Find the first order…

Answered: 10. Find and Classify all critical…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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The curve ax4+bx3+cx2+dx+k passes thru P1 (5, –210), has a critical point at P2 (4, –416), and an inflection point at P3 (2, 0) where a,b,c,d,k are non zero constants. 1. What are the values of a,b,c,d,k? 2. What type of critical point is P2?
The functions f(x, y) = x 2 + y 2 and g(x, y) = x 2 - y 2 both have acritical point at (0, 0). How is the behavior of the two functions at the critical point different?
Determine a,b,c and d so that the curve y=ax^3 + bx^2 + cx + d will have a critical point at (0,-2) and also tangent to the line 3x+y+3=0 at (-1,0)
construct 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. 2.dxdt=−x3+2y3,dydt=−2xy2; stable (at least)dxdt=−x3+2y3,dydt=−2xy2; stable at least
What values of a and b make ƒ(x) = x3 + ax2 + bx have a local minimum at x = 4 and a point of inflection at x = 1?
Please kindly help to solve and explain. Thank you very much. 3) Find the critical points of f(x,y) = xy2 + x2y + 8xy and classify each as a local maximum, local minimum, or saddle point.
construct 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 manufacturer incurs the following costs in producing x water ski vests in one day, for 0<x<150: fixed costs, $500; unit production cost, $25 per vest; equipment maintenance and repairs, 0.05x2 dollars. So, the cost of manufacturing x vests in one given day is given by C(x)=0.05x2+25x+500,where 0<x<150. a.) What is the average cost C(x) per vest if x vests are produced in one day? b.) Find the critical numbers of C(x), the intervals on which the average cost per vest is decreasing, the intervals on which the average cost per vest is increasing, and the local extrema.
A manufacturer incurs the following costs in producing x water ski vests in one day, for 0<x<200: fixed costs, $245; unit production cost, $15 per vest; equipment maintenance and repairs, 0.05x2 dollars. So, the cost of manufacturing x vests in one given day is given by C(x)=0.05x2+15x+245, where 0<x<200. (A) What is the average cost C(x) per vest if x vests are produced in one day? (B) Find the critical numbers of C(x), the intervals on which the average cost per vest is decreasing, the intervals on which the average cost per vest is increasing, and the local extrema. Do not graph
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10. Find and Classify all critical points of flx,y)=-x + Xy +3y-Sx-Ay +2. 2 for