Nagwa uses cookies to ensure you get the best experience on our website. Learn more about our Privacy Policy.

Lesson: Monotonicity of a Function

Worksheet • 25 Questions

Q1:

Find the intervals on which the function 𝑓 ( π‘₯ ) = 2 𝑒 βˆ’ 3 𝑒 + 4 π‘₯ π‘₯ is either increasing or decreasing.

  • AThe function is increasing on ο€Ό βˆ’ ∞ , ο€Ό 4 3   l n and ο€Ό ο€Ό 4 3  , ∞  l n .
  • BThe function is increasing on ο€Ό βˆ’ ∞ , ο€Ό 3 4   l n and ο€Ό ο€Ό 3 4  , ∞  l n .
  • CThe function is decreasing on ο€Ό βˆ’ ∞ , ο€Ό 4 3   l n and ο€Ό ο€Ό 4 3  , ∞  l n .
  • DThe function is decreasing on ( βˆ’ ∞ , ∞ ) .
  • EThe function is increasing on ( βˆ’ ∞ , ∞ ) .

Q2:

Find all possible intervals on which the function 𝑓 ( π‘₯ ) = π‘₯ βˆ’ 4 π‘₯ + 1 2 2 is increasing and decreasing.

  • A The function is decreasing on ( βˆ’ ∞ , 0 ) , and increasing on ( 0 , ∞ ) .
  • B The function is decreasing on ( βˆ’ ∞ , βˆ’ 1 ) , and increasing on ( βˆ’ 1 , ∞ ) .
  • C The function is decreasing on ( 0 , ∞ ) , and increasing on ( βˆ’ ∞ , 0 ) .
  • D The function is decreasing on ( 1 , ∞ ) , and increasing on ( βˆ’ ∞ , 1 ) .
  • E The function is decreasing on ( βˆ’ ∞ , 1 ) , and increasing on ( 1 , ∞ ) .

Q3:

Find the intervals on which the function 𝑓 ( π‘₯ ) = 4 π‘₯ π‘₯ 2 l n is increasing and decreasing.

  • AThe function is increasing on ο€Ώ 1 √ 𝑒 , ∞  and decreasing on ο€Ώ 0 , 1 √ 𝑒  .
  • BThe function is increasing on ο€½ 0 , 𝑒  βˆ’ 3 2 and decreasing on ο€½ 𝑒 , ∞  βˆ’ 3 2 .
  • CThe function is increasing on ο€Ώ 0 , 1 √ 𝑒  and decreasing on ο€Ώ 1 √ 𝑒 , ∞  .
  • DThe function is increasing on ο€½ 𝑒 , ∞  βˆ’ 3 2 and decreasing on ο€½ 0 , 𝑒  βˆ’ 3 2 .
  • EThe function is increasing on ο€Ί √ 𝑒 , ∞  and decreasing on ο€Ί 0 , √ 𝑒  .
Preview