Question 1

Which of the following best describes the main focus of Math 110 - Applied Calculus for Business at HACC?

Accepted Answer

A course focused on quadratic, polynomial, rational, exponential, and logarithmic functions, as well as differential and integral calculus with applications to business and economics.

Question 2

Which of the following is NOT a learning outcome for Math 110 as described in the syllabus?

Accepted Answer

Develop advanced programming algorithms for calculus applications.

Question 3

Suppose a business uses the cost function $$C(x) = 500 + 20x$$, where $$x is $$the number of units produced. What is the marginal cost, and what does it represent?

Accepted Answer

The marginal cost is $$20$$, representing the cost to produce one additional unit.

Question 4

Given the function $$f(x) = x^2$ + 3x + 2$$, what is the derivative $$f'(x)$$?

Accepted Answer

$$f'(x) = 2x + 3$$

Question 5

A company’s revenue function is $$R(x) = 100x - x^2$. What is the maximum revenue, and at what value of x$ does it occur?

Accepted Answer

Maximum revenue is $$2500 at$$ $$x = 50.$$

Question 6

Which of the following is the correct formula for the derivative of an exponential function $$f(x) = e$$^{kx}$$?

Accepted Answer

$$f'(x) = k e$$^{kx}$$

Question 7

If $$f(x, y) = x^2$ + y^2$, what are the critical points and what do they represent in a business context?

Accepted Answer

The critical point is at $$(0, 0)$$, representing a minimum cost or loss.

Question 8

Which of the following best describes the concept of consumer surplus in economics?

Accepted Answer

The area between the demand curve and the price line, above the equilibrium price.

Question 9

Evaluate the following limit: $$\lim_{x 	o 0} \frac{e^x - 1}{x}.$$

Accepted Answer

$$1$$

Question 10

A business wants to maximize profit, given by $$P(x) = -2x^2$ + 40x - 100. $$What is the optimal number of units $$x to $$produce for maximum profit?

Accepted Answer

$$x = 10$$

Question 11

Which of the following is the correct integral for finding the area under the curve $$y = 3x^2$ from x = 1$ to x = 4$?

Accepted Answer

$$\int_{1}^{4} 3x^2$ \, dx$$

Question 12

If $$f(x) = \ln(x)$$, what is $$f'(x)$$?

Accepted Answer

$$f'(x) = \frac{1}{x}$$

Question 13

A company’s demand function is $$p = 50 - 2x. $$What is the elasticity of demand when $$x = 10$$?

Accepted Answer

Elasticity $$E = \frac{d x}{d p} \cdot \frac{p}{x} = -0.4$$

Question 14

Which of the following is a correct application of the product rule for differentiation for $$f(x) = u(x)v(x)$$?

Accepted Answer

$$f'(x) = u'(x)v(x) + u(x)v'(x)$$

Question 15

Suppose a business’s profit function is $$P(x) = -x^2$ + 12x - 20. $$What is the maximum profit?

Accepted Answer

Maximum profit is $$16.$$

Question 16

Which of the following best describes a saddle point for a function of two variables?

Accepted Answer

A point where the function has a minimum in one direction and a maximum in another.

Question 17

If $$f(x) = 5x^3$ - 2x^2$ + x - 7$$, what is $$f''(x)$$?

Accepted Answer

$$f''(x) = 30x - 4$$

Question 18

A business uses the revenue function $$R(x) = 60x - 0.5x^2$. What is the marginal revenue when x = 20$?

Accepted Answer

Marginal revenue is $$R'(x) = 60 - x$$, so $$R'(20) = 40.$$

Question 19

Which of the following is the correct antiderivative of $$f(x) = 4x^3$?

Accepted Answer

$$\int 4x^3$ \, dx = x^4$ + C$$

Math 110 - Applied Calculus for Business: Course Syllabus and Structure

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