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Lesson: Consequences of Differentiability

Sample Question Videos

Worksheet • 12 Questions • 1 Video

Q1:

The graph of the first derivative of a continuous function is shown. On what intervals is increasing or decreasing?

  • A is increasing on the intervals and and decreasing on the intervals and .
  • B is increasing on the intervals and and decreasing on the intervals and .
  • C is increasing on the intervals and and decreasing on the intervals and .
  • D is increasing on the intervals and and decreasing on the intervals , , and .
  • E is increasing on the intervals , , and and decreasing on the intervals and .

Q2:

Let . Determine the intervals where this function is increasing and where it is decreasing.

  • A The function is decreasing on and and increasing on .
  • B The function is decreasing on and increasing on and .
  • C The function is decreasing on and increasing on and .
  • D The function is decreasing on and and increasing on .
  • E The function is decreasing on and and increasing on .

Q3:

The graph of the first derivative of a continuous function is shown. On what intervals is increasing or decreasing?

  • A is increasing on the intervals , , and and decreasing on the intervals and .
  • B is increasing on the intervals and and decreasing on the intervals and .
  • C is increasing on the intervals and and decreasing on the intervals , , and .
  • D is increasing on the interval and decreasing on the intervals and .
  • E is increasing on the intervals and and decreasing on the interval .

Q4:

The graph of a function 𝑦 = 𝑓 ( π‘₯ ) is shown. At which point are d d 𝑦 π‘₯ and d d 2 2 𝑦 π‘₯ both positive?

  • Apoint 𝐡
  • Bpoint 𝐸
  • Cpoint 𝐴
  • Dpoint 𝐷
  • Epoint 𝐢

Q5:

The graph of a function 𝑦 = 𝑓 ( π‘₯ ) is shown. At which point are d d 𝑦 π‘₯ and d d 2 2 𝑦 π‘₯ both negative?

  • Apoint 𝐸
  • Bpoint 𝐡
  • Cpoint 𝐴
  • Dpoint 𝐷
  • Epoint 𝐢

Q6:

Determine the intervals on which the function 𝑓 ( π‘₯ ) = βˆ’ π‘₯ βˆ’ 8 π‘₯ 2 is increasing and where it is decreasing.

  • Aincreasing over ] βˆ’ ∞ , βˆ’ 4 [ , decreasing over ] βˆ’ 4 , ∞ [
  • Bdecreasing over ] βˆ’ ∞ , βˆ’ 4 [ , increasing over ] βˆ’ 4 , ∞ [
  • C decreasing over ℝ
  • D increasing over ℝ

Q7:

Determine the intervals on which is concave up and concave down.

  • A The function is concave up on the interval and concave down on the interval .
  • B The function is concave up on the interval and concave down on the interval .
  • C The function is concave up on the interval and concave down on the interval .
  • D The function is concave up on the interval and concave down on the interval .
  • E The function is concave up on the interval and concave down on the interval .

Q8:

Determine the intervals on which the function is concave up and down.

  • A The function is concave down on and concave up on .
  • B The function is concave down on and concave up on .
  • C The function is concave down on and concave up on .
  • D The function is concave down on and and concave up on .
  • E The function is concave down on and concave up on .

Q9:

Which of the following statements is true for the function 𝑦 = 4 βˆ’ 6 π‘₯ + 3 π‘₯ 2 ?

  • AThe function is increasing on ] 1 , ∞ [ and decreasing on ] βˆ’ ∞ , 1 [ .
  • BThe function is decreasing on ] 1 , ∞ [ and increasing on ] βˆ’ ∞ , 1 [ .
  • CThe function is increasing on ℝ .
  • DThe function is decreasing on ℝ .

Q10:

Which of the following statements is true for the function β„Ž ( π‘₯ ) = βˆ’ π‘₯ βˆ’ 2 π‘₯ + 1 2 ?

  • A β„Ž ( π‘₯ ) is increasing on ] βˆ’ ∞ , βˆ’ 1 [ and decreasing on ] βˆ’ 1 , ∞ [ .
  • B β„Ž ( π‘₯ ) is increasing on ] βˆ’ ∞ , 2 [ and decreasing on ] 2 , ∞ [ .
  • C β„Ž ( π‘₯ ) is increasing on ] βˆ’ 1 , ∞ [ and decreasing on ] βˆ’ ∞ , βˆ’ 1 [ .
  • D β„Ž ( π‘₯ ) is increasing on ] 1 , ∞ [ and decreasing on ] βˆ’ ∞ , 1 [ .
  • E β„Ž ( π‘₯ ) is increasing on ] βˆ’ ∞ , 1 [ and decreasing on ] 1 , ∞ [ .

Q11:

Which of the following statements is true for the function 𝑔 ( π‘₯ ) = βˆ’ π‘₯ βˆ’ 1 4 π‘₯ βˆ’ 4 7 2 ?

  • A 𝑔 ( π‘₯ ) is increasing on ] βˆ’ ∞ , βˆ’ 7 [ and decreasing on ] βˆ’ 7 , ∞ [ .
  • B 𝑔 ( π‘₯ ) is increasing on ] βˆ’ ∞ , 2 [ and decreasing on ] 2 , ∞ [ .
  • C 𝑔 ( π‘₯ ) is increasing on ] βˆ’ 7 , ∞ [ and decreasing on ] βˆ’ ∞ , βˆ’ 7 [ .
  • D 𝑔 ( π‘₯ ) is increasing on ] 7 , ∞ [ and decreasing on ] βˆ’ ∞ , 7 [ .
  • E 𝑔 ( π‘₯ ) is increasing on ] βˆ’ ∞ , 7 [ and decreasing on ] 7 , ∞ [ .

Q12:

Let . Determine the intervals where this function is increasing and where it is decreasing.

  • A The function is decreasing on and and increasing on .
  • B The function is decreasing on and increasing on and .
  • C The function is decreasing on and increasing on and .
  • D The function is decreasing on and and increasing on .
  • E The function is decreasing on and and increasing on .
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