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Does a differentiable function have to have a relative minimum between any two relative maximum?
Yes.
What is an extreme value in a set?
the maximum or minimum value of a continuous function on a set.
Is a function that is continuous over a finite closed interval not have a maximum or a minimum value over that interval?
A function that is continuous over a finite closed interval must have both a maximum and a minimum value on that interval, according to the Extreme Value Theorem. This theorem states that if a function is continuous on a closed interval ([a, b]), then it attains its maximum and minimum values at least once within that interval. Therefore, it is impossible for a continuous function on a finite closed interval to not have a maximum or minimum value.
How can a quadratic function have both a maximum and a minimum point?
A quadratic function can only have either a maximum or a minimum point, not both. The shape of the graph, which is a parabola, determines this: if the parabola opens upwards (the coefficient of the (x^2) term is positive), it has a minimum point; if it opens downwards (the coefficient is negative), it has a maximum point. Therefore, a quadratic function cannot exhibit both extreme values simultaneously.
If f is continuous for all x and y and has two relative minima then f must have at least one relative maximum?
Yes.If you find 2 relative minima and the function is continuous, there must be exactly one point between these minima with the highest value in that interval. This point is a relative maxima.Think of temperature for example (it is continuous).
Does a differentiable function have to have a relative minimum between any two relative maximum?
Yes.
What is an extreme value in a set?
the maximum or minimum value of a continuous function on a set.
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.
How do you get a maximum displacement?
To determine the maximum displacement, you need to calculate the peak value of the displacement function. This is done by finding the extreme values (maximum or minimum) of the function, typically by taking the derivative and setting it to zero to find critical points. Once you have these critical points, evaluate the function at those points to find the maximum displacement.
How can a quadratic function have both a maximum and a minimum point?
A quadratic function can only have either a maximum or a minimum point, not both. The shape of the graph, which is a parabola, determines this: if the parabola opens upwards (the coefficient of the (x^2) term is positive), it has a minimum point; if it opens downwards (the coefficient is negative), it has a maximum point. Therefore, a quadratic function cannot exhibit both extreme values simultaneously.
What is maximum or minimum of function?
Addition is the maximum or minimum function in math.
What are math extremes?
In short, math extreme is the highest (or lowest) value of a math function on an interval (a,b). For example, function y=x2 has minimum (extreme) for x=0 on interval (minus infinity, plus infinity). Similarly, function y=-x2 has maximum (extreme) for x=0 on the same interval. Some functions have multiple extremes, which are called local extremes, but this is enough for basic understanding of the principle.
What is the maximum number of electrons that are contained in as s orbital?
An s orbital can have a maximum of two electrons.
If f is continuous for all x and y and has two relative minima then f must have at least one relative maximum?
Yes.If you find 2 relative minima and the function is continuous, there must be exactly one point between these minima with the highest value in that interval. This point is a relative maxima.Think of temperature for example (it is continuous).
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.
How do you find the minimum or maximum of a function?
By taking the derivative of the function. At the maximum or minimum of a function, the derivative is zero, or doesn't exist. And end-point of the domain where the function is defined may also be a maximum or minimum.
Does every graph of a cubic function have relative maximum and minimum points?
No, since the equation could be y = x3 (or something similar) which will have a point of inflection at (0,0), meaning there is no relative maximum/minimum, as the graph doesn't double back on itself For those that are unfamiliar with a point of inflection <http://mathsfirst.massey.ac.nz/Calculus/SignsOfDer/images/Introduction/POIinc.png>
