Homework

Task 1

a) Solve the quadratic equation x2 + 3x - 4 = 0

b) The abbreviation fraction ! !"#

!!"$!

c) The derivative function f(x)=3x3 +x2 -6x+ x+lnx+e2

d) Perform the polynomial division (x3 + 2x2 -13x +10): (x -1) e) A share is purchased for 112. Then the value increases by 5.5%. Then we get a decrease of 7%. And finally, it increases by 8.2%. What is the value of the stock after the changes?

f) Determine ò 1 (x3 +2x)dx

g) Use the definition of the derivative and show that for f (x) = 5x2 then f '(x) = 10x

Task 2

The costs of a business are given by the function K(x) = 0.2x2 +18x + 2000

And the income is given by the function I(x) = -0,1x2 +80x

For both functions, xÎ[0.200] applies a) Find an expression for the profit function (also called the profit function). b) Find the coverage points (where cost is equal to income). c) How many units must the company produce and sell in order for it to be as large as possible profit? d) Find the expression for the marginal cost and the marginal revenue. e) Calculate how many units the marginal cost is 22 and explain in words what that means the marginal cost is 22 for a given number of units. f) Find an expression for the unit cost A (x) and find the production quantity that gives the lowest unit cost.

Task 3

The function f (x) is given by f(x)=x3 -2x2

a) Find the zeros of f (x)

b) Calculate f (x)

c) Find by calculation any top and bottom points on the graph of f (x) d) Find the equation for the inversion of f (x) by calculation. Task 4 A function f is given by

f(x,y)=x3 +y3 -3xy+9

a) Find the partially derived of the first and second order for f (x, y). b) Find the stationary points and classify them.