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1. Suppose that a quantiies q and q2, respectively, and that it sells them at prices...
Question 6 (1 point) Suppose a function f(x) is differentiable everywhere and has a local minimum...
Question 6 (1 point) Suppose a function f(x) is differentiable everywhere and has a local minimum at x=c. If f(x)<O when x<c, and f'(x)>0 when x>c, then by the Global Interval Method we know x=c is O a local maximum an absolute maximum a local minimum an absolute minimum
4. Consider the following function in R" f(Fi, n)=-1) k-1 Find the critical point of this...
4. Consider the following function in R" f(Fi, n)=-1) k-1 Find the critical point of this function and show whether it is a local minimum, a local maximum, or neither 5. By examining the Hessian matrix, show that if f(x,y, ) has a local minimum at then g(z, y,) -f(x,y, ) must have a local maximum at that point. Likewise, show that if f has a local maximum, then g must have a local minimum at that point. (ro, yo,...
3 Ltuts.),)wher F.,and v are differentiable. Suppose also that (-2-)1 (-2-3)--101, u (-2-3)-4, x ...
3 Ltuts.),)wher F.,and v are differentiable. Suppose also that (-2-)1 (-2-3)--101, u (-2-3)-4, x (-2-3)--5 F (L-7)-3, F(-2-3)-3, F(I.-7)-2, and F.(-2-3)-0. Find W (-2-3 Circle your answer below o w(-2-3)-2 (e) W(-2-3)-12 ( W(-2-3)-14 (g) W(-2-3)-35 (h) W (-2,-3)-199 W(-2,-3)-202 M x2 + xy + y2 + 3y the local maximum and minimum values of the function f(x,y) 4. Find . Circle your answer below. (a) Relative minimum f(1.-2)--3, and no relative maximum. (b) No relative minimum, and relative maximum...
Calculus 4 Let f(x,y) = A)-i-j E) i+j 1. Find the gradient vector Vf (1, 1)...
Calculus 4
Let f(x,y) = A)-i-j E) i+j 1. Find the gradient vector Vf (1, 1) at the point (x,y) = (1,1). B) - 1 - 1 D)-i-j 10. . Find the largest value of the directional derivative of the function f(x,y) = ry + 2ya at the point (3,y) = (1,2). A) 53 ' B) V58 C) V63 D) 74 E) 85 y + The function (,y) = 2 + y2 + A) (-3,5), saddle point C) (-1,3), maximum...
#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 a...
#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...
I cannot figure out the first set of critical points and classifications. (1 point) The following...
I cannot figure out the first
set of critical points and classifications.
(1 point) The following table gives values of the differentiable function y = f(x). X 0 1 2 3 4 5 6 7 8 9 10 y 1 -1 -3 -2 1-1 -2 123 5 Estimate the x-values of critical points of f(x) on the interval 0<x< 10. Classify each critical point as a local maximum, local minimum, or neither. (Enter your critical points as comma-separated xvalue,classification pairs....
Suppose the production function of a firm is given by q = L1/4K1/4. The prices of...
Suppose the production function of a firm is given by q = L1/4K1/4. The prices of labor and capital are given by w = $10 and r = $20, respectively. a) Write down the firm's cost minimization problem. b) What returns to scale does the production function exhibit? Explain c) What is the Marginal Rate of Technical Substitution (MRTS) between capital and labor? d) What is the optimal capital to labor ratio? Show your work. e) Derive the long run...
Suppose we are looking for the point on the plane x + 2y + z =...
Suppose we are looking for the point on the plane x + 2y + z = 5 closest to the point (2,3,0). Which of the following approaches DOES NOT lead to the answer? = 0 Solve the system of equationsJ 2(x - 2) - 2(5 - x - 2y) | 2(y-3) - 4(5 - x - 2y) = 0 Find the intersection point of the line r(t) = (2+ t, 3 + 2t, t) with the given plane. 2(x 2...
. Suppose the production function of a firm is given by q = L1/4K2/4. The prices of labor and cap...
. Suppose the production function of a firm is given by q = L1/4K2/4. The prices of labor and capital are given by and w = $9 and r = $18, respectively. Derive the long run cost function. Show your work. What happens to the firm’s average cost as it increases production and why? Derive the firm’s long run supply function. What will be the quantity of output that maximizes the firm’s profit when the price of output is $1?...
The demand equation for your company's virtual reality video headsets is 2,000 where q is the tot...
The demand equation for your company's virtual reality video headsets is 2,000 where q is the total number of headsets that your company can sell in a week at a price of p dollars. The total manufacturing and shipping cost amounts to $130 per headset (a) Find the weekly cost, revenue and profit as a function of the demand q for headsets. C(4)- R(q) (b) How many headsets should your company sell to maximize profit? (Give your answer to the...
Question 6 (1 point) Suppose a function f(x) is differentiable everywhere and has a local minimum at x=c. If f(x)<O when x<c, and f'(x)>0 when x>c, then by the Global Interval Method we know x=c is O a local maximum an absolute maximum a local minimum an absolute minimum
4. Consider the following function in R" f(Fi, n)=-1) k-1 Find the critical point of this function and show whether it is a local minimum, a local maximum, or neither 5. By examining the Hessian matrix, show that if f(x,y, ) has a local minimum at then g(z, y,) -f(x,y, ) must have a local maximum at that point. Likewise, show that if f has a local maximum, then g must have a local minimum at that point. (ro, yo,...
3 Ltuts.),)wher F.,and v are differentiable. Suppose also that (-2-)1 (-2-3)--101, u (-2-3)-4, x (-2-3)--5 F (L-7)-3, F(-2-3)-3, F(I.-7)-2, and F.(-2-3)-0. Find W (-2-3 Circle your answer below o w(-2-3)-2 (e) W(-2-3)-12 ( W(-2-3)-14 (g) W(-2-3)-35 (h) W (-2,-3)-199 W(-2,-3)-202 M x2 + xy + y2 + 3y the local maximum and minimum values of the function f(x,y) 4. Find . Circle your answer below. (a) Relative minimum f(1.-2)--3, and no relative maximum. (b) No relative minimum, and relative maximum...
Calculus 4
Let f(x,y) = A)-i-j E) i+j 1. Find the gradient vector Vf (1, 1) at the point (x,y) = (1,1). B) - 1 - 1 D)-i-j 10. . Find the largest value of the directional derivative of the function f(x,y) = ry + 2ya at the point (3,y) = (1,2). A) 53 ' B) V58 C) V63 D) 74 E) 85 y + The function (,y) = 2 + y2 + A) (-3,5), saddle point C) (-1,3), maximum...
#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...
I cannot figure out the first
set of critical points and classifications.
(1 point) The following table gives values of the differentiable function y = f(x). X 0 1 2 3 4 5 6 7 8 9 10 y 1 -1 -3 -2 1-1 -2 123 5 Estimate the x-values of critical points of f(x) on the interval 0<x< 10. Classify each critical point as a local maximum, local minimum, or neither. (Enter your critical points as comma-separated xvalue,classification pairs....
Suppose we are looking for the point on the plane x + 2y + z = 5 closest to the point (2,3,0). Which of the following approaches DOES NOT lead to the answer? = 0 Solve the system of equationsJ 2(x - 2) - 2(5 - x - 2y) | 2(y-3) - 4(5 - x - 2y) = 0 Find the intersection point of the line r(t) = (2+ t, 3 + 2t, t) with the given plane. 2(x 2...
The demand equation for your company's virtual reality video headsets is 2,000 where q is the total number of headsets that your company can sell in a week at a price of p dollars. The total manufacturing and shipping cost amounts to $130 per headset (a) Find the weekly cost, revenue and profit as a function of the demand q for headsets. C(4)- R(q) (b) How many headsets should your company sell to maximize profit? (Give your answer to the...
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