Question 1

Which of the following best describes the graph of the function $$f(x) = x^2$?

Accepted Answer

A parabola opening upward with vertex at $$(0,0).$$

Question 2

Given the function $$f(x) = e^x$$, what is the slope of the tangent line at $$x = 0$$?

Accepted Answer

$$1$$

Question 3

Which of the following functions has a domain of all real numbers except $$x = 0$$?

Accepted Answer

$$f(x) = \dfrac{1}{x}$$

Question 4

If $$f(x) = x^3$ - 3x$$, which of the following points is a local maximum?

Accepted Answer

$$(-\sqrt{1}, f(-\sqrt{1}))$$

Question 5

Which of the following is the correct derivative of $$f(x) = \sqrt{x}$$?

Accepted Answer

$$f'(x) = \dfrac{1}{2\sqrt{x}}$$

Question 6

A business finds its revenue function is $$R(x) = 100x - x^2$. What is the maximum revenue?

Accepted Answer

$$R(50)$$

Question 7

Which of the following integrals represents the area under the curve $$y = x^2$ from x = 0$ to x = 2$?

Accepted Answer

$$\$$int_0$$^2 x^2$ \, dx$$

Question 8

If $$f(x) is $$continuous and differentiable, which of the following statements is always true?

Accepted Answer

$$f(x)$$ has a tangent line at every point in its domain.

Question 9

Which of the following is the antiderivative of $$f(x) = 2x$$?

Accepted Answer

$$x^2 + C$

Question 10

A company’s cost function is $$C(x) = 50 + 10x. $$What is the marginal cost?

Accepted Answer

$$10$$

Question 11

Which graph best represents the function $$f(x) = |x|$$?

Accepted Answer

A V-shaped graph opening upward with vertex at $$(0,0).$$

Question 12

Evaluate $$\$$int_0$$^1 x \, dx.$$

Accepted Answer

$$\dfrac{1}{2}$$

Question 13

Which of the following functions is NOT differentiable at $$x = 0$$?

Accepted Answer

$$f(x) = |x|$$

Question 14

If $$f(x) = x^2$ - 4x + 3$$, what is the minimum value of $$f(x)$$?

Accepted Answer

$$-1$$

Question 15

Which of the following is the correct integral for the area between $$y = x^2$ and y = x$ from x = 0$ to x = 1$?

Accepted Answer

$$\$$int_0$$^1 (x - x^2$) \, dx$$

Question 16

A company’s profit function is $$P(x) = -2x^2$ + 40x - 100. $$How many units $$x$$ should be produced to maximize profit?

Accepted Answer

$$x = 10$$

Question 17

Which of the following is the correct derivative of $$f(x) = e$$^{2x}$$?

Accepted Answer

$$2e^{2x}$$

Question 18

If $$f(x) = \dfrac{1}{x}$$, what is $$f'(x)$$?

Accepted Answer

$$-\dfrac{1}{x^2$}$$

Question 19

Evaluate $$\$$int_0$$^2 (3x^2$ - 2x) \, dx.$$

Accepted Answer

$$8$$

Question 20

Which of the following best describes the graph of $$f(x) = -x^2$?

Accepted Answer

A parabola opening downward with vertex at $$(0,0).$$

Business Calculus Final Review: Functions, Derivatives, and Integration

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