Test B Review, Calculator may be used, whichever is simpliest please show me thanks

Question

Answer 1

33).

The function f(x) = y = 0.5x⁴ - 2.5x³ + 0.5x² + 10.5x + k.

Observe the graph of the function, the graph crosses the x - axes at x = 1.

So, the x - intercept is 1.

Then, f(1) = 0.

f(1) = 0.5(1)⁴ - 2.5(1)³ + 0.5(1)² + 10.5(1) + k = 0

0.5(1)⁴ - 2.5(1)³ + 0.5(1)² + 10.5(1) + k = 0

0.5 - 2.5 + 0.5 + 10.5 + k = 0

9 + k = 0

k = - 9.

Therefore, the value of k = - 9.

Solution : Option (c) is the correct choice.

Answer 2

34).

Cost of producing x items : C(x) = 20,000 + 5(x - 60)².

Revenue by selling x items : R(x) = 15,000 + 130x.

The revenue will exceed the cost for all x values means : R(x) > C(x).

(15,000 + 130x) > [20,000 + 5(x - 60)²]

Apply formula : (a - b)² = a² - 2ab + b².

(15,000 + 130x) > [20,000 + 5(x² - 120x + 3600)]

(15,000 + 130x) > [20,000 + 5x² - 600x + 18000]

(15,000 + 130x) > [5x² - 600x + 38000]

[5x² - 600x + 38000] < (15,000 + 130x)

[5x² - 600x - 130x - 15000 + 38000] < 0

[5x² - 730x + 23000] < 0

[x² - 146x + 4600] < 0

[x² - 46x - 100x + 4600] < 0

[x(x - 46) - 100(x - 46)] < 0

(x - 46)(x - 100) < 0

46 < x < 100.

Solution : Option (d) is the correct choice.

Answer 3

35).

If we substitute 0 for delta x then the Function changes to 0/0 format.

Apply L - Hospital Rule.

Apply limits to the function.

.

Therefore,  .

Solution : Option (b) is the correct choice.