1.What is the integral from a to d equal to?

Answer: 5 - 4 + 1 = 2

2.Find an equation of the tangent to the curve y(x) =x- 5x + 4 at the point (1, 1).

Answer: y'(x) = 2x - 5; y'(1) = 2*1 - 5 = -3 is the slope.

Plug in m=-3 and (1, 1) into (y - y1) =m(x - x1) and the final answer is y + 3x = 4.

3.Integrate 3e^x

Answer:

4.Which of the labeled points in the graph are inflection points?

Answer:b, d, h

5.Integrate 10

Answer:

6.What is the definite integral of a positive function f(x) from a to b calculating?

Answer: Area

7.Find all critical points and global extremes of f(x) = x -e^xon the entire real number line.

Answer: f'=1-e^x=0 at x=0. (0, -1) is a critical point and global maximum because f'(-1)>0 and f'(1)<0. Once we have a critical point, we need to check how is the f' behaving at x before and after x=0. Since the f' change the sign from + to -, it is a maximum at x=0.

8.Integrate (5 - 4x)

Answer: 5x - 2x^2 + C

9.Determine all critical points for the function f(x) = x^3 + 9x^2 + 6.

Answer: f'(x) = 3x^2 + 18x; f'(x) = 0 @ x=0 and x=-6

10.Integrate 1/x from 1 toe

Answer:

11.Write an integral of a region bounded by f(x) = x/3, the x axis, line x=0 and line x=3.

Answer:

12.Find the area between x1 = 1 and x2 = 4 if y is between 0 and 3

Draw the two vertical lines x1 = 1 and x2 = 4 and two horizontal lines y=0 and y=3. You will get a square. The area of that square is 3*3 = 9

Answer: 9

13.If s = 6t^2 - 10t + 9 represents the position of an object at time t, find the acceleration (s") of this object at t = 3 sec.

Answer: find the second derivative; s'' = 12, therefore the acceleration is 12.

14.Calculate where the minimum value of the cost function C(x) = 25x^2 - 1500x + 30000 occurs and what that minimum value is.

Answer: The derivative of C is C'(n) = 50n - 1500. Set it equal to 0: 50n - 1500 = 0 and we get n = 30. It is minimum because C" = 50>0.C(30) = 7500

15.Find the area between graph y=3x^2 and the horizontal axis for x between 1 and 2

Answer:

16.Find P(n) such that P'(n) = 3x + 4x andP(2) = 20

Integrate P'(n) and get P(n)=x^3 + 2x^2 + C

We knowP(2) is 20. Plug 2 in P(n) and solve for C:

2^3 + 2*2^2 + C = 20

C=4

Answer: P(n) = x^3 + 2x^2 + 4

17.Find the area between w(x) =3x +12and z(x) = x -3x +12if 0 x 6.

Answer:

18.Suppose MR(q) is the marginal revenue when selling q number of items. Thentheintegral of MR(q) from 0 to 50 represents the total revenue from the sale of50items.True or False?

Answer: True

19.Find the second derivative of the function y = 4x+ 3x-9.

Answer: y' = 8x + 3; y'' = 8

20.The cost, in thousands of dollars, for producing x thousandiphonesis given by C(x)= -x/100 + 2x + 95. Find the value that best approximates the average cost when 3 thousandiphonesare produced.

Average cost is C(x) / x =C(3) / 3 = 100.91 / 3 = 33.64

Answer: 33.64

21.Suppose the demand for a productis given by p=d(q) = -0.5q + 140 and the supply for the same product is given by p=s(q) =3q. For both functions, q is the quantity and p is the price in dollars.

a.Find the equilibrium point

b.Find the consumer surplus at the equilibrium price.

c.Find the producer surplus at the equilibrium price.

Answer a:Solve -0.5q + 140 =3q. The q =40. Whenqis40, we get thatp= 120. Equilibrium point(40, 120)

Answer b:solve the following expression

Answer C:solve the following expression