The integrating factor for the differential equation  is

Multiplying the differential equation by

we obtain

Then, by integrating both sides of this equation, we have

where we have used integration by parts on the last term in the above equation. Thus the general solution of the differential equation is

maximum {-3,1,-3}=1, minimum {4,5,3}=3 and 1+3=4.

To obtain a solution to the linear equations above let us multiply second equation with 3 and add two equalities:

which gives

If we substitute this value into second equation we obtain

Therefore the correct answer is C.

Because the intersection point of these lines is

the point

must also provide both  of the equations. Hence we obtain

Then one gets

x - y = 4          -x + y = -4

x - 2y = 10       x - 2y = 10              

y = -6,   x – 2(-6) =10,  x = -2,  (-2, -6)

To find the maximum value we need to substitute each corner point to the goal function. Observe that for the point (0, 0) we have

for the point (-7, 0) we have

 for the point (0, -4) we have

for the point (-3, -1) we have

Hence the maximum point is 24 and the correct option is C.

the correct answer is B.

The only point satisfying

The correct answer is A.

For the point (2, 3),

F = 12x + 2y = 12.2 - 2.3 = 30

Since

one has

Using the formula for the present value of money we write

So the correct answer is A.

Correct answer is B .

Considering

The antiderivative of 

where c is an arbitrary real number. For F (-1) =4 we have F(-1) =3/8+c=4 which gives c=29/8.

(1,1) , F = 4.1 – 1.1 = 3, 

(1,4) , F = 4.1 – 1.4 = 0, 

(2,6) , F = 4.2 – 1.6 = 2, 

(4,9) , F = 4.4 – 1.9 = 7,  max value = 7

Arranging given function, we have

Since the graph of passes through the point we get

2=F(0)=0³+0²-0+c ⇒ c=2.

Hence f(x)=x³+x²-x+2