JAMIA 2025 — Mathematics PYQ
JAMIA | Mathematics | 2025If a function f(x) is increasing, then its derivative must be:
Choose the correct answer:
- A.
Positive
(Correct Answer) - B.
Negative
- C.
Zero
- D.
None of these
Positive
Explanation
Mathematical Solution:
Ek function f(x) ke increasing hone ki condition niche di gayi hai:
f′(x)≥0
Key Rules:
-
Strictly Increasing: Agar function hamesha badh raha hai, toh uska derivative zero se bada hota hai:
f'(x) > 0 -
Non-decreasing: Agar function badh raha hai ya kahin constant bhi hai, toh:
f′(x)≥0
Final Answer:
The derivative must be greater than or equal to zero (f′(x)≥0).
Explanation
Mathematical Solution:
Ek function f(x) ke increasing hone ki condition niche di gayi hai:
f′(x)≥0
Key Rules:
-
Strictly Increasing: Agar function hamesha badh raha hai, toh uska derivative zero se bada hota hai:
f'(x) > 0 -
Non-decreasing: Agar function badh raha hai ya kahin constant bhi hai, toh:
f′(x)≥0
Final Answer:
The derivative must be greater than or equal to zero (f′(x)≥0).