Quiz about AB Calculus Exam Review (Graphs and Tables) #1

Question 1

The graph of a function g has horizontal tangents at x = 4 and x = 8 as shown. If $$f\left(x\right)=\int_0^{\sqrt[]{x}}g\left(t\right)dt,$$ what is the value of $$f$$

Accepted Answer

$$\frac{1}{2}$$

Answer

$$0$$

Answer

$$\frac{3}{4}$$

Answer

$$1$$

Question 2

The graph of y = f(x) consists of three line segments as shown. If the average value of f on the interval [0, 5] is 1, what is the value of k?

Accepted Answer

$$\frac{4}{5}$$

Answer

$$\frac{3}{5}$$

Answer

$$\frac{7}{10}$$

Answer

$$\frac{9}{10}$$

Question 3

If f is a function such that for $$a for $$b

Accepted Answer

Option B is correct

Answer

A.

Answer

C.

Answer

D.

Question 4

The graph of a function f is shown. Which of the following statements must be false?

Accepted Answer

$$f$$ exists.

Answer

f(x) is defined for $$0\le x\le b.$$

Answer

$$f\left(b\right)$$ exists.

Answer

$$\lim_{x\rightarrow a^-}\ f$$ exists.

Question 5

If a trapezoidal sum underapproximates $$\int_a^bf\left(x\right)dx,$$ and a right Riemann sum overapproximates $$\int_a^bf\left(x\right)dx,$$ which of the following could be the graph of $$y=f\left(x\right)?$$

Accepted Answer

Option B is correct

Answer

A.

Answer

C.

Answer

D.

Question 6

Some values of a differentiable function f are shown in the table. What is the approximate value of $$f$$

Accepted Answer

13

Answer

8

Answer

10

Answer

16

Question 7

Let f be a twice differentiable function with and for all x, in the closed interval [2, 8]. Which of the following could be a table of values for f?

Accepted Answer

Option A is correct

Answer

B.

Answer

C.

Answer

D.

Question 8

Which of the following is the area of the shaded region shown in the figure?

Accepted Answer

$$\int_0^a\left[b-g\left(x\right)+f\left(x\right)\right]dx$$

Answer

$$\int_0^a\left[g\left(x\right)-f\left(x\right)\right]dx$$

Answer

$$\int_0^a\left[b+g\left(x\right)-f\left(x\right)\right]dx$$

Answer

$$\int_0^a\left[b-g\left(x\right)-f\left(x\right)\right]dx$$

Question 9

The graph of the function f is shown. Which of the following statements about f is not true?

Accepted Answer

$$\lim_{x\rightarrow b}f\left(x\right)=1$$

Answer

$$\lim_{x\rightarrow a}f\left(x\right)=3$$

Answer

$$f\left(a\right)=4$$

Answer

$$f\left(b\right)=2$$

Question 10

The graph of $$f$$ the derivative of the function f, is shown. If f is a twice differentiable function, which of the following statements must be true?

I. $$f\left(a\right)>f\left(b\right)$$

II. The graph of f has a point of inflection at $$x=b.$$

III. The graph of f is concave down on the interval $$a

Accepted Answer

II and III only

Answer

I only

Answer

II only

Answer

III only

Question 11

The figure shows the graph of the function $$f\left(x\right)=\frac{\left(x-2\right)^2}{2}$$ and the graph of g which is tangent to the graph of f at the point (4, 2). If $$h\left(x\right)=f\left(g\left(x\right)\right),$$ what is $$h$$

Accepted Answer

0

Answer

-4

Answer

-2

Answer

2

AB Calculus Exam Review (Graphs and Tables) #1

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