1. The integral of y = ex is 2. If f(x) and g(x) have the same integral then: f(

Question

1. The integral of y = ex is

2. If f(x) and g(x) have the same integral then:

f(x) must be equal to g(x)

f(x) and g(x) differ by a constant

Neither A nor B is true

Nothing definite can be said about f(x) and g(x) anything could be the case

3.If d2y/dx2 = 2 then which of the following is a possible value for the function y?

y = x2 + x + 1

y = x2 + 2x + 2

y = x2 + 3x + 3

All of A, B and C

None of A, B and C

4.If we know the marginal revenue then to find the revenue function we must integrate the marginal revenue function.

False

5. f'(x) = 4x2 -8x and f(0) = 6. Find f(4). Give your answer correct to two decimal places.

6. f'(x) = 2x+8 and f(1) = 11. Find f(4)

7. R''(x) = 15-0.6x, R'(12) = 105. Find R(2). Give your answer correct to two decimal places.

8. f''(x) = 3x-6, f(0) = 5. f'(0) = 7. Find f(5). Give your answer correct to two decimal places.

A.

f(x) must be equal to g(x)

B.

f(x) and g(x) differ by a constant

C.

Neither A nor B is true

.

Nothing definite can be said about f(x) and g(x) anything could be the case

3.If d2y/dx2 = 2 then which of the following is a possible value for the function y?

A.

y = x2 + x + 1

B.

y = x2 + 2x + 2

C.

y = x2 + 3x + 3

D.

All of A, B and C

None of A, B and C

4.If we know the marginal revenue then to find the revenue function we must integrate the marginal revenue function.

True

False

5. f'(x) = 4x2 -8x and f(0) = 6. Find f(4). Give your answer correct to two decimal places.

6. f'(x) = 2x+8 and f(1) = 11. Find f(4)

7. R''(x) = 15-0.6x, R'(12) = 105. Find R(2). Give your answer correct to two decimal places.

8. f''(x) = 3x-6, f(0) = 5. f'(0) = 7. Find f(5). Give your answer correct to two decimal places.

Explanation / Answer

1) y = ex

Integrating on both sides

==> y = ex = ex +c

2) f(x) and g(x) differ by a constant

3) d2y/dx2 = 2

==> dy/dx = 2x + c1

==> y = 2(x2/2) + c1x + c2

==> y = x2 + c1x + c2

All A,B,C are possible

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