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A relative (or local) maximum, for a function, is a point such that the value of the function at that point is greater than the values within a region on either side of it. It need not be a global maximum.
For example, consider a functions such as f(x) = 3*x - x^3
[it is shaped a bit like the letter S on its side].
Now f(1) = 2 is greater than all values of f(x) for x > -2. So the point (1, f(1)0 represents a relative maximum. However, for any x less than -2, f(x) is greater than f(1), and as x becomes more and more negative, f(x) becomes infinitely large. So f(1) cannot be a global maximum.
What else can I help you with?
Does a differentiable function have to have a relative minimum between any two relative maximum?
Yes.
What is relative maximum in math?
In mathematics, a relative maximum (or local maximum) refers to a point in a function's domain where the function value is greater than the values of the function at nearby points. Specifically, if ( f(x) ) is a function, then ( f(a) ) is a relative maximum if there exists an interval around ( a ) such that ( f(a) \geq f(x) ) for all ( x ) in that interval. Relative maxima are important in calculus and optimization, as they indicate points where a function reaches a peak within a specific range.
What is the maximum number of relative extreme contained in the graph of this function xxx plus X?
To find the maximum number of relative extrema of the function ( f(x) = x^3 + x ), we first compute its derivative: ( f'(x) = 3x^2 + 1 ). Since ( f'(x) ) is always positive (as ( 3x^2 + 1 > 0 ) for all ( x )), the function is strictly increasing and does not have any relative extrema. Therefore, the maximum number of relative extrema contained in the graph of this function is zero.
Why relative frequency maximum probability?
Relative frequency refers to the proportion of times an event occurs compared to the total number of trials. It is often used to estimate the probability of an event based on observed data. The maximum probability occurs when the relative frequency of an event approaches 1, indicating that the event is almost certain to happen based on empirical observations. Therefore, relative frequency provides a practical way to gauge the likelihood of an event occurring in the long run.
A fisherman travels downstream at full speed to?
The maximum speed that a vessel will achieve relative to ground is its own maximum speed through water plus the speed of the the moving water downstream.
What is the maximum value of a wave reaches relative to its resting position?
The maximum value a wave reaches relative to its resting position is called the amplitude. It represents the maximum displacement of the wave from its equilibrium position.
Does a differentiable function have to have a relative minimum between any two relative maximum?
Yes.
The height of a plant is 45 cm with an estimated absolute error of 0.9 cm what percent is the relative error?
To get the relative error is the maximum error over the measurement. So the maximum error is the absolute error divided by 2. So the maximum error is 0.45. The relative error is 0.45 over 45 cm.
What is relative maximum in math?
In mathematics, a relative maximum (or local maximum) refers to a point in a function's domain where the function value is greater than the values of the function at nearby points. Specifically, if ( f(x) ) is a function, then ( f(a) ) is a relative maximum if there exists an interval around ( a ) such that ( f(a) \geq f(x) ) for all ( x ) in that interval. Relative maxima are important in calculus and optimization, as they indicate points where a function reaches a peak within a specific range.
What is the maximum value a wave reaches relative to its resting position?
The maximum value a wave reaches relative to its resting position is called the amplitude. Amplitude represents the maximum displacement of a wave from its equilibrium position. It is a measure of the wave's intensity or strength.
What is the percentage of water vapor a certain volume of air contains relative to the maximum amount?
The percentage of water vapor in a certain volume of air relative to the maximum amount it can hold is referred to as the relative humidity. It is calculated by taking the actual amount of water vapor present in the air, dividing it by the maximum amount the air can hold at that temperature, and then multiplying by 100. For instance, if the air contains 10 grams of water vapor, and the maximum capacity at that temperature is 20 grams, the relative humidity would be 50%.
What are extremes in math?
the first or the last term of a proportion or series. a relative maximum or relative minimum value of a function in a given region.
What is the relative humidity outside?
The relative humidity outside is the amount of water vapor in the air compared to the maximum amount the air can hold at its current temperature.
Air that holds the maximum amount of water at a given temperature is said to be what?
Relative Humidity.
What is relative intensity?
Relative intensity refers to the level of effort or exertion required to perform an activity, relative to an individual's maximum capacity. It is often used in exercise science to prescribe and monitor the intensity of workouts based on a percentage of an individual's maximum effort. Understanding relative intensity helps tailor training programs to achieve specific fitness goals.
What is the maximum number of relative extreme contained in the graph of this function xxx plus X?
To find the maximum number of relative extrema of the function ( f(x) = x^3 + x ), we first compute its derivative: ( f'(x) = 3x^2 + 1 ). Since ( f'(x) ) is always positive (as ( 3x^2 + 1 > 0 ) for all ( x )), the function is strictly increasing and does not have any relative extrema. Therefore, the maximum number of relative extrema contained in the graph of this function is zero.
What is the proportion of water vapor present in a parcel of air relative to the maximum amount of water vapor that could be present in the air at the same temperature?
The relative humidity.
