Chapter 2: Differentiation

Chapter 2: Differentiation

1. Find the slope of the tangent line to the graph of the function below at the given point.

f (x) 2x ?10, (3, ?4) A) 2 B) ?2 C) ?10 D) 12 E) none of the above Ans: A

2. Find the slope of the tangent line to the graph of the function at the given point.

f (x) ?5x2 +10, (?2, ?10) A) 20 B) ?5 C) ?10 D) ?20 E) none of the above Ans: A

3. Find the slope of the tangent line to the graph of the function at the given point.

f (x) 2x2 + 6, (3, 24) A) 12 B) 2 C) ?6 D) 18 E) none of the above Ans: A

4. Use the limit definition to find the slope of the tangent line to the graph of f (x) 4x 29 at the point (5, 7) . A) 2 7 B) 2 7 C) 1 7 D) 1 7 E) 1 5 Ans: A

Larson, Calculus: An Applied Approach (+Brief), 9e Page 59

5. Find the derivative of the following function using the limiting process.

f (x) ?2x2 ? 9x

A) ?2 B) ?4x ? 9 C) ?4x + 9 D) ?4x E) none of the above Ans: B

6. Find the derivative of the following function using the limiting process.

f (x) 9x ? 6 A) f (x) 9

2 9x ? 6 B) f (x) 9

2 9x ? 6

C) f (x) 9 9x ? 6 1/2

2 D) f (x) 9

9x ? 6 E) either B or D Ans: A

7. Find the derivative of the following function using the limiting process.

f (x) 2 x?9

A)

f

(

x)

x

2 ?9

2

B)

f

(

x)

x

2 +9

2

C)

f

(

x)

x

2 +

9

D)

f

(

x)

x

2 ?9

2

E) none of the above Ans: D

Larson, Calculus: An Applied Approach (+Brief), 9e Page 60

8. Find an equation of the line that is tangent to the graph of f and parallel to the given line. f (x) 5x2 , 20x y 2 0 A) y 20x ? 20 B) y 20x + 20 C) y ?20x + 20 D) y ?20x ? 20 E) none of the above Ans: A

9. Find an equation of the a line that is tangent to the graph of f and parallel to the given line. f (x) 5x3 , 135x y 6 0 A) y ?135x ? 270 B) y 135x + 270 C) y ?135x + 270 D) y 135x ? 270 E) both B and D Ans: E

Larson, Calculus: An Applied Approach (+Brief), 9e Page 61

10. Identify a function f (x) that has the given characteristics and then sketch the function. f (0) 3; f '(x) 4, x A) f (x) 4x 3

B) f (x) ?4x 3

C) f (x) 4x 3

Larson, Calculus: An Applied Approach (+Brief), 9e Page 62

D) f (x) ?4x 3 E) f (x) 3x + 4

Larson, Calculus: An Applied Approach (+Brief), 9e Page 63

Ans: A 11. Find the derivative of the function.

f (x) x7 A) f (x) 7x7 B) f (x) 7x6 C) f (x) 6x6 D) f (x) 6x8 E) none of the above Ans: B 12. Find the derivative of the function. f (x) 2x3 ? 3x2 +1 A) f (x) 6x2 ? 6x B) f (x) 4x2 ? 3x C) f (x) 4x ? 3x2 D) f (x) 6x2 ? 6x +1 E) none of the above Ans: A

Larson, Calculus: An Applied Approach (+Brief), 9e Page 64

13. For the function given, find

f (x) x3 15x 6

A) x2 15 B) 3x2 6 C) 3x2 15 D) 3x3 15x E) x3 15x 6 Ans: C

f '(x).

14. Find the derivative of the function. h(x) 15x23 11x13 4x10 3x 7

A) 330x22 132x12 36x9 3 B) 345x23 143x13 40x10 3x C) 15x22 11x12 4x9 3 D) 345x22 143x12 40x9 3 E) 330x23 132x13 36x10 3x Ans: D

15. Find the derivative of the function h(x) x5/3 .

A) h '(x) 5 x8/3 3

B) h '(x) 5 x2/3 3

C) h '(x) 5 x2/3 3

D) h '(x) 5 x8/3 3

E) h '(x) 5 x2/3 3

Ans: C

16. Find the derivative of the function s(t) 2x2 8 .

A)

s '(t)

4 x3

B) s '(t) 4 x3

C)

s

'(t)

4 x3

8

D)

s '(t)

4 x3

8

E) s '(t) 2x3

Ans: B

Larson, Calculus: An Applied Approach (+Brief), 9e Page 65

17. Find the derivative of the function.

f

(x)

1 x3

A)

f

( x)

2 x4

B) f (x) 3 x2

C)

f

( x)

3 x4

D)

f

( x)

4 x4

E) none of the above

Ans: C

18. Differentiate the given function.

y

3 4x4

A) 12 x5

B) 3 x4

C) 12 x4

D) 3 x5

E) 4 x5

Ans: D

19. Differentiate the given function.

y

5 (4x)4

A) 80

(4 x)5

B) 20 (4x)5

C) 80 (4x)5

D) 20

(4 x)5

E) 20 (4x)3

Ans: C

Larson, Calculus: An Applied Approach (+Brief), 9e Page 66

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