Question
Download Solution PDFThe function f(x) = x2 − 2x is strictly decreasing in the interval
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFConcept:
For a function y = f(x):
- At the points of local maxima or minima, f'(x) = 0.
- In the regions where f(x) is increasing, f'(x) > 0.
- In the regions where f(x) is decreasing, f'(x) < 0.
Calculation:
For the function f(x) = x2 - 2x to be strictly increasing, f'(x) > 0.
For the function f(x) = x2 − 2x to be strictly decreasing, f'(x) < 0.
⇒ f'(x) = 2x - 2 < 0
⇒ x < 1
⇒ x ∈ (−∞, 1)
Last updated on Jul 4, 2025
-> The CUET 2025 provisional answer key has been made public on June 17, 2025 on the official website.
-> The CUET 2025 Postponed for 15 Exam Cities Centres.
-> The CUET 2025 Exam Date was between May 13 to June 3, 2025.
-> 12th passed students can appear for the CUET UG exam to get admission to UG courses at various colleges and universities.
-> Prepare Using the Latest CUET UG Mock Test Series.
-> Candidates can check the CUET Previous Year Papers, which helps to understand the difficulty level of the exam and experience the same.