Question 1

Refer to the graph with labeled points A, B, and C. Which labeled region is most likely to contain a root of the function shown?

Accepted Answer

Region A

Question 2

Given the graph with points A, B, and C, which region must contain a root of the function according to the Intermediate Value Theorem?

Accepted Answer

Region C

Question 3

In the secant line diagram, what does the slope of the secant line between points $$(a, f(a))$$ and $$(b, f(b))$$ represent?

Accepted Answer

The average rate of change between $$a$$ and $$b$$

Question 4

Using the population table, during which interval did the human population experience the largest average rate of change?

Accepted Answer

Between 2011 and 2020

Question 5

In the secant line diagram with points $$(x_0$, f(x_0$))$$ and $$(x_0$ + h, f(x_0$ + h))$$, what happens to the secant line as $$h 	o 0$$?

Accepted Answer

It becomes the tangent line at $$x_0$$

Question 6

Given the table of $$f(x)$$, $$f'(x)$$, $$g(x)$$, and $$g'(x)$$, what is the value of $$h'(1) if$$ $$h(x) = (x + g(x$$))^{-2}$$?

Accepted Answer

$$-0.125$$

Question 7

Given the same table, what is $$h'(3) if$$ $$h(x) = \left(\frac{f(x)}{g(x)}\$$right)^2$$?

Accepted Answer

$$-1.5$$

Question 8

In the baseball diamond diagram, if a batter hits a ball toward third base at 75 ft/s and runs toward first base at 24 ft/s, what is the rate at which the distance between the ball and the batter is changing two seconds after the ball is hit?

Accepted Answer

$$\approx 80.0 ft/s$$

Question 9

In the elliptical cell diagram, what is the slope of the tangent line at the point $$(x_p, y_p) on $$the ellipse $$\frac{x^2$}{100} + \frac{y^2$}{25} = 1$$?

Accepted Answer

$$-\frac{y_p}{4x_p}$$

Question 10

In the differential diagram, what does $$dy = f'(a)dx$$ represent?

Accepted Answer

The approximate change in $$y$$ for a small change in $$x$$

Question 11

In the exponential growth/decay diagram, what does the family of solutions $$y = Ce$$^{kt}$$ represent when k$$ \u003e 0$$?

Accepted Answer

Exponential growth

Calculus Study Notes: Limits, Continuity, Differentiation, and Applications

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