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Monotonic Functions Video Lecture | Mathematics for IIT JAM, GATE, CSIR NET, UGC NET
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FAQs on Monotonic Functions Video Lecture - Mathematics for IIT JAM, GATE, CSIR NET, UGC NET
| 1. What is a monotonic function? |  |
Ans. A monotonic function is a mathematical function that either always increases or always decreases as its input value increases. In other words, the function either consistently rises or consistently falls without any fluctuations.
| 2. How can we determine the monotonicity of a function? | |
Ans. To determine the monotonicity of a function, we need to analyze its derivative. If the derivative is always positive, then the function is strictly increasing. If the derivative is always negative, then the function is strictly decreasing. If the derivative is zero at some points, it indicates that there may be local extrema.
| 3. Can a function be both increasing and decreasing? | |
Ans. No, a function cannot be both increasing and decreasing at the same time. By definition, a function is either increasing or decreasing. However, it is possible for a function to be non-monotonic, where it is neither strictly increasing nor strictly decreasing.
| 4. Are all linear functions monotonic? | |
Ans. Yes, all linear functions are monotonic. Linear functions have a constant rate of change, meaning they either strictly increase or strictly decrease. The slope of a linear function determines its monotonicity.
| 5. Can a function be monotonically increasing in one interval and monotonically decreasing in another interval? | |
Ans. Yes, it is possible for a function to be monotonically increasing in one interval and monotonically decreasing in another interval. When a function changes its monotonicity at a specific point or interval, it is called a point of inflection. This occurs when the derivative of the function changes sign, indicating a shift in the direction of monotonicity.
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Dec 23, 2024 Last updated |
Video Description: Monotonic Functions for Mathematics 2024 is part of Mathematics for IIT JAM, GATE, CSIR NET, UGC NET preparation.
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