Differentiate from first principles

Question 1

Using first principles, f(x) = −2x² + x gives (f(x + h) − f(x))/h = −4x − 2h + 1. What is f′(x)?

Answer 

Question 2

For f(x) = x² − 6x, simplify (f(x + h) − f(x))/h.

• A. 2x − 6
• B. 2xh + h²
• C. 2x + h² − 6
• D. 2x + h − 6

Question 3

Using first principles, f(x) = −5x² + 3x gives (f(x + h) − f(x))/h = −10x − 5h + 3. What is f′(x)?

Answer 

Question 4

For f(x) = x² − 6x, simplify (f(x + h) − f(x))/h.

• A. 2x − 6
• B. 2x + h − 6
• C. x² + h − 6
• D. 2x + h² − 6

Question 5

Using first principles, f(x) = 4x² − 5x gives (f(x + h) − f(x))/h = 8x + 4h − 5. What is f′(x)?

Answer 

Question 6

For f(x) = x² + 4x, simplify (f(x + h) − f(x))/h.

• A. 2x + h + 4
• B. x² + h + 4
• C. 2x + h² + 4
• D. 2x + 4

Question 7

Using first principles, f(x) = −2x² + 2x gives (f(x + h) − f(x))/h = −4x − 2h + 2. What is f′(x)?

Answer 

Question 8

For f(x) = x² + 2x, simplify (f(x + h) − f(x))/h.

• A. 2x + h + 2
• B. x² + h + 2
• C. 2xh + h²
• D. 2x + 2

Question 9

Using first principles, f(x) = −2x² − 3x gives (f(x + h) − f(x))/h = −4x − 2h − 3. What is f′(x)?

Answer 

Question 10

For f(x) = x² − 4x, simplify (f(x + h) − f(x))/h.

• A. 2x − 4
• B. 2xh + h²
• C. 2x + h − 4
• D. x² + h − 4

Question 11

Using first principles, f(x) = −2x² − 3x gives (f(x + h) − f(x))/h = −4x − 2h − 3. What is f′(x)?

Answer 

Question 12

For f(x) = x² + 6x, simplify (f(x + h) − f(x))/h.

• A. x² + h + 6
• B. 2xh + h²
• C. 2x + h + 6
• D. 2x + h² + 6

Question 13

Using first principles, f(x) = −2x² + x gives (f(x + h) − f(x))/h = −4x − 2h + 1. What is f′(x)?

Answer 

Question 14

For f(x) = x² + 3x, simplify (f(x + h) − f(x))/h.

• A. 2x + 3
• B. 2x + h + 3
• C. 2x + h² + 3
• D. x² + h + 3

Question 15

Using first principles, f(x) = 3x² − 2x gives (f(x + h) − f(x))/h = 6x + 3h − 2. What is f′(x)?

Answer 

Question 16

For f(x) = x², simplify (f(x + h) − f(x))/h.

• A. 2x + h²
• B. 2x + h
• C. 2xh + h²
• D. x² + h