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Increasing and Decreasing Functions at a Point Video Lecture | Mathematics (Maths) Class 12 - JEE

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FAQs on Increasing and Decreasing Functions at a Point Video Lecture - Mathematics (Maths) Class 12 - JEE

1. What is the definition of an increasing function at a point?
Ans. An increasing function at a point is a function in which the values of the function are greater as the input values increase. In other words, if the function f(x) is increasing at a point a, it means that for any two values, a and b, where a < b, the value of f(a) is less than or equal to f(b).
2. How can we determine if a function is increasing or decreasing at a specific point?
Ans. To determine if a function is increasing or decreasing at a specific point, we can analyze the behavior of the function's derivative at that point. If the derivative is positive, the function is increasing at that point. If the derivative is negative, the function is decreasing at that point.
3. What does it mean for a function to be decreasing at a point?
Ans. A function is said to be decreasing at a point if the values of the function decrease as the input values increase. In other words, if the function f(x) is decreasing at a point a, it means that for any two values, a and b, where a < b, the value of f(a) is greater than or equal to f(b).
4. Can a function be both increasing and decreasing at the same point?
Ans. No, a function cannot be both increasing and decreasing at the same point. A function can be either increasing or decreasing at a specific point, but not both simultaneously. This is because the definition of an increasing function contradicts the definition of a decreasing function.
5. How can we determine if a function has a maximum or minimum at a specific point?
Ans. To determine if a function has a maximum or minimum at a specific point, we can analyze the behavior of the function's derivative around that point. If the derivative changes sign from positive to negative, the function has a maximum at that point. If the derivative changes sign from negative to positive, the function has a minimum at that point.
204 videos|288 docs|139 tests

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