The question is not clear. A function is defined by an equation and that requires an equals sign. there is no equals sign in the question. It is therefore impossible to give a proper answer to your question. Please resubmit your question spelling out the symbols as "plus", "minus", "times", "divided by", "equals".
Assuming the standard x and y axes, the range is the maximum value of y minus minimum value of y; and the domain is the maximum value of x minus minimum value of x.
Standard notation for a quadratic function: y= ax2 + bx + c which forms a parabola, a is positive , minimum value (parabola opens upwards on an x-y graph) a is negative, maximum value (parabola opens downward) See related link.
Surely, you should check the value of the function at the boundaries of the region first. Rest depends on what the function is.
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.
pi value= 1
Both the function "cos x" and the function "sin x" have a maximum value of 1, and a minimum value of -1.
the maximum or minimum value of a continuous function on a set.
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.
In Calculus, to find the maximum and minimum value, you first take the derivative of the function then find the zeroes or the roots of it. Once you have the roots, you can just simply plug in the x value to the original function where y is the maximum or minimum value. To know if its a maximum or minimum value, simply do your number line to check. the x and y are now your max/min points/ coordinates.
That refers to the highest and lowest value of a function. A "local maximum" (or local minimum) refers to a value that is higher than any near-by value, for a certain neighborhood.
An argmax is a mathematical term for the argument of the maximum - the set of points of a given argument for which a given function attains its maximum value.
You cannot. The function f(x) = x2 + 1 has no real zeros. But it does have a minimum.
Assuming the standard x and y axes, the range is the maximum value of y minus minimum value of y; and the domain is the maximum value of x minus minimum value of x.
At the maximum point of a function, the value of the second derivative is less than or equal to zero. Specifically, if the second derivative is negative, it indicates that the function is concave down at that point, confirming a local maximum. If the second derivative equals zero, further analysis is needed to determine the nature of the critical point, as it may be an inflection point or a higher-order maximum.
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.
In mathematics, the term "maximum" refers to the largest value in a given set of numbers or the highest point of a function within a specified domain. It can be used in various contexts, such as finding the maximum value of a dataset, the maximum height of a curve, or the optimal solution in optimization problems. The maximum can be either absolute (the highest value overall) or relative (the highest value in a local neighborhood).
If x2 is negative it will have a maximum value If x2 is positive it will have a minimum value