Question 1

Given the function $$f(x) = x^2$ - 6$$, what is the simplified form of $$f(x + h) - f(x)$$?

Accepted Answer

$$2xh + h^2$

Question 2

For the linear function $$f(x) = 5x - 5$$, what is the value of $$\frac{f(x + h) - f(x)}{h}$$?

Accepted Answer

$$5$$

Question 3

A box is constructed by cutting squares of side $$x$$ from each corner of a $$10$$ inch by $$12$$ inch sheet and folding up the sides. What is the volume $$V(x) of $$the box in terms of $$x$$?

Accepted Answer

$$V(x) = x(12 - 2x)(10 - 2x)$$

Question 4

What is the domain of the volume function $$V(x) = x(12 - 2x)(10 - 2x)$$, given the physical restrictions of the box?

Accepted Answer

$$0 \u003c x \u003c 5$$

Question 5

Given the linear equation $$y = 3x - 9$$, what is the $$x-$$intercept?

Accepted Answer

$$x = 3$$

Question 6

For the function $$f(x) = x^2$ - 6$$, what is the average rate of change from $$x = 2 to$$ $$x = 5$$?

Accepted Answer

$$7$$

Question 7

If $$f(x) = 5x - 5$$, what is the $$y-$$intercept of the function?

Accepted Answer

$$-5$$

Question 8

A company models its profit $$P(x) by$$ $$P(x) = 2x^2$ - 8x + 10$$, where $$x is $$the number of units sold. What is the profit when $$x = 3$$?

Accepted Answer

$$P(3) = 4$$

Question 9

Given $$f(x) = x^2$ - 6$$, which of the following represents the difference quotient $$\frac{f(x + h) - f(x)}{h}$$?

Accepted Answer

$$\frac{2xh + h^2$}{h}$$

Question 10

A business finds that its revenue $$R(x) is $$given by $$R(x) = 100x - 2x^2$, where x$ is the number of items sold. What is the maximum possible revenue?

Accepted Answer

$$2500$$

Question 11

For the function $$f(x) = 5x - 5$$, what is the slope?

Accepted Answer

$$5$$

Question 12

Suppose the cost $$C(x) to $$produce $$x$$ units is $$C(x) = 4x + 20. $$What is the marginal cost?

Accepted Answer

$$4$$

Question 13

If $$f(x) = x^2$ - 6$$, what is the value of $$f(4)$$?

Accepted Answer

$$10$$

Question 14

A company wants to maximize the volume of a box made from a $$10$$ inch by $$12$$ inch sheet by cutting squares from each corner. What value of $$x ($$side of the square) gives the maximum volume?

Accepted Answer

$$x = 2$$

Question 15

Given the function $$f(x) = x^2$ - 6$$, which of the following is the correct graph of $$f(x)$$?

Accepted Answer

A parabola opening upwards with vertex at $$(0, -6)$$

Question 16

If the revenue function is $$R(x) = 100x - 2x^2$, at what value of x$ is the revenue maximized?

Accepted Answer

$$x = 25$$

Question 17

For the function $$f(x) = 5x - 5$$, what is the equation in slope-intercept form?

Accepted Answer

$$y = 5x - 5$$

Question 18

A company’s cost function is $$C(x) = 4x + 20. $$What is the cost to produce $$10$$ units?

Accepted Answer

$$60$$

Question 19

Given $$f(x) = x^2$ - 6$$, what is the $$y-$$intercept?

Accepted Answer

$$-6$$

Question 20

If $$f(x) = x^2$ - 6$$, what is the slope of the tangent line at $$x = 2$$?

Accepted Answer

$$4$$

Fundamental Concepts in Business Calculus: Functions, Difference Quotients, and Applications

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