Question 1

Given the function $$f(x) = x^2$ + 5x - 6$$, what are the $$x-$$intercepts of the graph?

Accepted Answer

$$(1, 0)$$ and $$(-6, 0)$$

Question 2

For the function $$f(x) = x^2$ + 5x - 6$$, what is the $$y-$$intercept?

Accepted Answer

$$(0, -6)$$

Question 3

What is the $$x-$$coordinate of the relative minimum of $$f(x) = x^2$ + 5x - 6$$?

Accepted Answer

$$x = -\frac{5}{2}$$

Question 4

Calculate the value of $$f(x) at $$its relative minimum for $$f(x) = x^2$ + 5x - 6.$$

Accepted Answer

$$-12.25$$

Question 5

For $$f(x) = x^2$ + 5x - 6$$, what is the value of the second derivative $$f''(x)$$?

Accepted Answer

$$2$$

Question 6

Given $$f(x) = (1 - 2x)^3$, what is the y$-intercept of the graph?

Accepted Answer

$$(0, 1)$$

Question 7

For $$f(x) = (1 - 2x)^3$, what is the x$-intercept?

Accepted Answer

$$(\frac{1}{2}, 0)$$

Question 8

What is the derivative $$f'(x) of$$ $$f(x) = (1 - 2x)^3$?

Accepted Answer

$$-6(1 - 2x)^2$

Question 9

At what $$x-$$value does $$f(x) = (1 - 2x)^3$ have a critical point?

Accepted Answer

$$x = \frac{1}{2}$$

Question 10

For $$f(x) = (1 - 2x)^3$, what is the value of the second derivative f$$''(x)$$ at x$$ = \frac{1}{2}$$?

Accepted Answer

$$0$$

Question 11

Which of the following best describes the critical point at $$x = \frac{1}{2}$$ for $$f(x) = (1 - 2x)^3$?

Accepted Answer

It is neither a minimum nor a maximum.

Question 12

Suppose you are sketching the graph of $$f(x) = x^2$ + 5x - 6$$ for a business profit model. What does the $$y-$$intercept represent in this context?

Accepted Answer

The profit when $$x = 0$$ units are sold.

Question 13

If $$f(x) = x^2$ + 5x - 6$$ models the cost of producing $$x$$ items, at which $$x-$$values does the cost become zero?

Accepted Answer

$$x = 1$$ and $$x = -6$$

Question 14

For $$f(x) = x^2$ + 5x - 6$$, what is the slope of the tangent line at $$x = 1$$?

Accepted Answer

$$7$$

Question 15

Which function has a point of inflection at $$x = \frac{1}{2}$$?

Accepted Answer

$$f(x) = (1 - 2x)^3$

Question 16

If $$f(x) = (1 - 2x)^3$ models the revenue from selling x$ units, what does the x$-intercept represent?

Accepted Answer

The break-even quantity.

Question 17

For $$f(x) = x^2$ + 5x - 6$$, what is the equation of the tangent line at $$x = 0$$?

Accepted Answer

$$y = 5x - 6$$

Question 18

Which of the following statements is true about the graph of $$f(x) = x^2$ + 5x - 6$$?

Accepted Answer

It has a relative minimum.

Question 19

For $$f(x) = (1 - 2x)^3$, what is the sign of the derivative f$$'(x)$$ for x$$ \u003c \frac{1}{2}$$?

Accepted Answer

Negative

Sketching Curves: Intercepts, Asymptotes, and Critical Points in Business Calculus

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