MOKAU MATEMATIKOS

Mokau matematikos moksleivius ir studentus, sprendziu uzdavinius.

1. Determine the ranks of the following matrices.
2. Determine the ranks of the following matrices for all values of parameters.
3. Determine the direction given of maximal increase from the point.
4. Find the directional derivative of f(x,y)=x^2 +2xy+ y^3 at the point (x,y)=(1;1) in the direction given by the vector b=(1;3).
5. Examine the convexity/concavity of the following functions.
6. Determine if the following functions are quasiconcave.
7. Find the leading priciple minor of the second order.
8. Nustatykite, kokia yra funkcija z=f(x,y) isgaubta, igaubta/tariamai isgaubta, tariamai igaubta.
9. Fixed costs for a certain comodity are 5000 Lt, variable costs per unit are 30 Lt. Selling price of the commodity is 50 Lt. Build up a profit equation and determine the marginal profit. What is the change in profit, if production volume increases from 100 to 110 units?
10. Determine the increase intervals of the function: y=x^2*e^(-2x).
11. The price a firm obtains far a commodity varies with demand Q according to the formula P(Q)=18-0,006Q. Total cost is C(Q)=0,004Q^2+4Q+4500. Find maximum profit.
12. Compute y’’ when xy=5.
13. The demands for a monopolist’s two products is determined by the equations p= 25-x, q=24-2y, where p and q are prices per unit of two goods, and x and y are the corresponding quantities. Suppose that the costs of producing and selling x units of the first good and y units of the second good are: C(x;y)= 3x^2+3xy+y^2 . (a) Find the monopolist’s profit Profit (x;y) from producing and selling x units of the first good and y units of the other.


L A Z D Y N A I

Kontaktiniai duomenys

Nuotraukos