Worksheet: Graphing Using Derivatives

In this worksheet, we will practice using derivatives to graph a function.

Q1:

Which of the following is the graph of 𝑓 ( 𝑥 ) = ( 𝑥 + 1 ) ( 𝑥 2 ) ?

  • A
  • B
  • C
  • D
  • E

Q2:

Consider the polynomial function whose graph 𝑦 = 𝑃 ( 𝑥 ) is given below.

Use the given points and the fact that 𝑥 = 1 is a critical point of the function 𝑃 to determine 𝑃 ( 𝑥 ) .

  • A 1 6 4 ( 𝑥 5 ) ( 𝑥 + 1 ) ( 3 𝑥 7 )
  • B 1 6 4 ( 𝑥 5 ) ( 𝑥 + 1 ) ( 3 𝑥 7 )
  • C 1 6 4 ( 𝑥 5 ) ( 𝑥 + 1 ) ( 3 𝑥 7 )
  • D ( 𝑥 5 ) ( 𝑥 + 1 ) ( 3 𝑥 7 )
  • E 1 6 4 ( 𝑥 5 ) ( 𝑥 + 1 ) ( 3 𝑥 7 )

Determine the intervals where 𝑃 ( 𝑥 ) < 1 .

  • A , 4 7 5 3 1 , 4 7 + 5 3
  • B 4 7 5 3 , 1 ( 1 , )
  • C 4 7 5 3 , 1 1 , 4 7 + 5 3
  • D 4 7 5 3 , 4 7 + 5 3
  • E , 4 7 5 3 4 7 + 5 3 ,

Q3:

Which of the following is the graph of the function 𝑓 ( 𝑥 ) = 𝑥 + 6 𝑥 9 𝑥 + 1 ?

  • A
  • B
  • C
  • D
  • E

Q4:

Which of the following could be the graph of the function 𝑓 ( 𝑥 ) = ( 𝑥 2 ) ? Use derivatives to sketch the function.

  • A
  • B
  • C
  • D
  • E

Q5:

Which of the following is the graph of the function 𝑓 ( 𝑥 ) = 1 1 0 𝑥 + 1 0 𝑥 ?

  • A
  • B
  • C
  • D
  • E

Q6:

Which of the following is the graph of the function 𝑓 ( 𝑥 ) = 𝑥 + 𝑥 6 ?

  • A
  • B