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

204 videos|288 docs|139 tests

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

1. What is an increasing function?
Ans. An increasing function is a mathematical function in which the value of the dependent variable (output) increases as the value of the independent variable (input) increases. In other words, as we move from left to right on the graph of an increasing function, the graph will go up.
2. What is a decreasing function?
Ans. A decreasing function is a mathematical function in which the value of the dependent variable (output) decreases as the value of the independent variable (input) increases. In other words, as we move from left to right on the graph of a decreasing function, the graph will go down.
3. How can we determine if a function is increasing or decreasing?
Ans. To determine if a function is increasing or decreasing, we can examine its derivative. If the derivative of a function is positive, then the function is increasing. If the derivative is negative, then the function is decreasing. If the derivative is zero, the function may have a local maximum or minimum.
4. Can a function be both increasing and decreasing?
Ans. No, a function cannot be both increasing and decreasing simultaneously. A function can either be increasing, where the values of the output increase as the input increases, or it can be decreasing, where the values of the output decrease as the input increases. It cannot exhibit both behaviors at the same time.
5. Are there any other ways to determine if a function is increasing or decreasing without using derivatives?
Ans. Yes, there are alternative methods to determine if a function is increasing or decreasing without using derivatives. One such method is to analyze the intervals of the function where the slope is positive or negative. If the slope is positive, the function is increasing, and if the slope is negative, the function is decreasing. Additionally, the behavior of the function at critical points, such as local maxima or minima, can also provide information about its increasing or decreasing nature.
204 videos|288 docs|139 tests

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