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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).
How do you calculate a range in mathematics?
Well... When you define a function, you're supposed to give it's domain and a set containing it's range with the definition. Sometimes these are implicit. For example, for the function square root, one assumes that the domain is the positive real numbers. The range is then also the positive real numbers. Generally, the easyest way to do it for an easy function is to draw a picture. If you're working with real to real functions, you just have to break the function into continuous pieces, and find the maximum and minimum of each piece. The range is then the union of all the intervals between the maxima and minima (it can be open intervals if the function tends asymptotically to it's maxima or minima without reaching them)
How do you find the range of a rational function?
If the degree of the polynomial is odd, the range is all real numbers - for example, y = x5. If the degree is even, use derivatives to find maxima or minima. You learn about derivatives, maxima and minima in any basic calculus course. Example: y = x4 - 3x3 Take the derivative: y' = 4x3 - 9x2 Solve for zero: 4x3 - 9x2 = 0 This will give you two maxima or minima; in this case, check at which of these points the function has the smallest value. Because of the positive coefficient of the leading term, the function values go from this point all the way to plus infinity.
What angle a body is projected to get maximam height?
45 degrees
How do you define fitness function in GAtool matlab?
x^2
