Calculus Test 3.1 And 3

Exam Name___________________________________

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Solve the problem. 1) A car's distance s in miles from its starting point after t hours is given by s(t) = 5t2

1)

Find the average rate of change of distance with respect to time (average velocity) as t changes from t1 = 5 to t2 = 7.

A) 35 miles/hr

B) 17.1 miles/hr

C) 60 miles/hr

Find an equation for the line tangent to the given curve at the indicated point. 2) y = x 2 - 4 at (-2, 0) A) y = -2x - 8

3) y = x 3 - 9x + 2 at (3, 2) A) y = 18x + 2

D) 30 miles/hr

B) y = -4x - 16

C) y = -4x - 8

D) y = -4x - 12

B) y = 20x - 52

C) y = 18x - 52

D) y = 2

2)

3)

Referring to the graph below, assign one of the following descriptors to the point: large positive slope, small positive slope, zero slope, small negative slope, large negative slope.

4) Q

5) R

A) zero slope C) small negative slope

B) small positive slope D) large negative slope

A) small negative slope C) small positive slope

B) large negative slope D) zero slope

4)

5)

Solve the problem.

6) Suppose that the dollar cost of producing x radios is c(x) = 200 + 10x - 0.2x 2 . Find the average cost per radio of producing the first 30 radios. A) $320.00 B) $2.00 C) $4.00 D) $120.00 1

6)

Graph the function and the indicated tangent line. 7) Graph f(x) = 4x 2 and the tangent line to the graph at the point whose x-coordinate is 1.

A)

B)

C)

D)

2

7)

Referring to the graph below, assign one of the following descriptors to the point: large positive slope, small positive slope, zero slope, small negative slope, large negative slope.

8) S

9) P

A) zero slope C) small negative slope

B) large positive slope D) large negative slope

A) small negative slope C) large negative slope

B) small positive slope D) large positive slope

8)

9)

OPEN ENDED QUESTIONS. Answer the following questions and show all necessary work to receive full credit. 10) Consider the curve f(x) in the accompanying sketch.

Find the slope of the tangent line at the point where x = 2. Enter your answer as just a fraction or an integer.

3

10)

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. For the graph, determine the value(s) of x for which f(x) is nondifferentiable. 11)

A) x = -3, x = 0, x = 3 C) x = -2, x = 2

11)

B) x = -2, x = 0, x = 2 D) x = -3, x = 3

12)

12)

A) x = -2, x = 2 C) x = -2, x = 0, x = 2

B) x = 2 D) x = 0

13)

13)

A) x = 0, x = 1, x = 2 C) x = 1

B) x = 0 D) x = 2

Solve the problem. 14) For the graph determine if f (x) is positive, negative, zero, or undefined at x = 3.

A) undefined

B) positive

C) zero

4

14)

D) negative

15) For the graph determine if f (x) is positive, negative, zero, or undefined at x = 4.

A) negative

B) zero

C) undefined

15)

D) positive

16) For the graph determine if f (x) is positive, negative, zero, or undefined at x = -2.

A) zero Find f'(x) at the given value of x. 17) f(x) = x3 + 6; Find f (5). A) 76

16)

B) positive

C) undefined

D) negative

B) 75

C) 81

D) -75

18) f(x) = 7 x; Find f (2). A) Does not exist

17)

18) B) 28

C)

5

7 2 2

D)

7 2 2

The graphs of a function f(x) and its derivative f'(x) are shown below. Decide which is the graph of f(x) and which is the graph of f'(x). 19) 19)

A) B) C) D)

Neither graph could be the derivative of the other. f(x) is the solid line; f'(x) is the dashed line. f(x) is the dashed line; f'(x) is the solid line. Either graph could be the derivative of the other.

6

Sketch the derivative of the graph. 20)

20)

A)

B)

C)

D)

7

21)

21)

A)

B)

C)

D)

Solve the problem.

22) The equation for free fall at the surface of Planet X is s = 6.21t2 m with t in seconds. Assume a rock is dropped from the top of a 600m cliff. Find the speed of the rock at t = 3 sec. A) 18.63 m/sec B) 37.26 m/sec C) 17.63 m/sec D) 38.26 m/sec

22)

OPEN ENDED QUESTIONS. Answer the following questions and show all necessary work to receive full credit. Find the slope of the curve at the general point, xo 23) y = 4x2 - 9x,

23)

8