Question 1

Given the function $$y = 2x^3$ - 7x^2$ - 6$$, what is the average rate of change of $$y$$ between $$x = -2$$ and $$x = 3$$?

Accepted Answer

$$18$$

Question 2

For the function $$f(x) = x^2$ + 2x$$, what is the instantaneous rate of change at $$x = 4$$?

Accepted Answer

$$10$$

Question 3

Given $$f(x) = x^3$ + 12 - 9x - 6$$, what is the instantaneous rate of change at $$x = -3$$?

Accepted Answer

$$-36$$

Question 4

Find the average rate of change of $$y = x^2$ between x = 1$ and x = 4$.

Accepted Answer

$$3$$

Question 5

A motorcycle traveling at speed $$v (in $$mph) when the brakes are applied has stopping distance $$d = 0.05v^2$. What is the instantaneous rate of change of distance with respect to velocity when v = 44$ mph?

Accepted Answer

$$4.4$$

Question 6

If $$f(x) = x^2$ + 2x$$, what is the average rate of change between $$x = 2$$ and $$x = 8$$?

Accepted Answer

$$12$$

Question 7

For the function $$y = 2x^3$ - 7x^2$ - 6$$, what is the instantaneous rate of change at $$x = 3$$?

Accepted Answer

$$15$$

Question 8

A company models its revenue with $$R(x) = x^2$ + 2x$$, where $$x is $$the number of units sold. What is the marginal revenue when $$x = 5$$?

Accepted Answer

$$12$$

Question 9

If $$f(x) = x^3$ + 12 - 9x - 6$$, what is the average rate of change between $$x = -3$$ and $$x = 0$$?

Accepted Answer

$$-18$$

Question 10

A car's stopping distance is modeled by $$d = 0.05v^2$. If the speed increases from 40$ mph to 44$ mph, what is the average rate of change of stopping distance with respect to speed?

Accepted Answer

$$4.3$$

Question 11

For $$y = x^2$, what is the instantaneous rate of change at x = 4$?

Accepted Answer

$$8$$

Question 12

A business models its cost function as $$C(x) = 2x^3$ - 7x^2$ - 6. $$What is the marginal cost at $$x = 2$$?

Accepted Answer

$$-6$$

Question 13

If $$f(x) = x^2$ + 2x$$, what is the instantaneous rate of change at $$x = 0$$?

Accepted Answer

$$2$$

Question 14

For the function $$y = x^2$, what is the average rate of change between x = 2$ and x = 5$?

Accepted Answer

$$6$$

Question 15

A motorcycle's stopping distance is $$d = 0.05v^2$. What is the instantaneous rate of change of d$ with respect to v$ at v = 30$ mph?

Accepted Answer

$$3$$

Business Calculus: Average and Instantaneous Rate of Change Practice Guidance

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