Suppose f(x,y)=x2+y2−2x−2y+1f(x,y)=x2+y2−2x−2y+1 (A) How many critical points does ff have in R2R2? (B) If there is a local minimum, what is the value of the discriminant D at that point? If there is none, type N. (C) If there is a local maximum, what is the value of the discriminant D at that point? If there is none, type N. (D) If there is a saddle point, what is the value of the discriminant D at that point? If there is none, type N. (E) What is the maximum value of ff on R2R2? If there is none, type N. (F) What is the minimum value of ff on R2R2? If there is none, type N.

Minimize ƒ(x, y, z) = xy + yz subject x2 + y2 - 2 = 0 and x2 + z2 - 2 = 0.

find the minimum and maximum value of the function on. the given interval by comparing values at the critical points and endpoints. y = −x , [0, 2] ln x, [1, 3]

Obtain the value of y and y’ at x = 2 from the particular solution indicated.

In the function:  f(x)= (3x^2)ln(x) , x>0  What are the critical numbers of the function?

The function f(x,y)=xy(1−5x−4y)   has 4 critical points. List them and select the type of critical point.

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

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.

Let y be the solution of the initial value problemy" +y = - sin(2x), y (0) = 0, y'(0) = 0.The maximum value of y is