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)(𝑥2)?

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

Q3:

Which of the following is the graph of the function 𝑓(𝑥)=𝑥+6𝑥9𝑥+1?

  • A
  • B
  • C
  • D
  • E

Q4:

Which of the following could be the graph of the function 𝑓(𝑥)=(𝑥2)? Use derivatives to sketch the function.

  • A
  • B
  • C
  • D
  • E

Q5:

Which of the following is the graph of the function 𝑓(𝑥)=110𝑥+10𝑥?

  • A
  • B
  • C
  • D
  • E

Q6:

Which of the following is the graph of the function 𝑓(𝑥)=𝑥+𝑥6?

  • A
  • B