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What is the maximum value that the graph of ycosx assume?
Both the function "cos x" and the function "sin x" have a maximum value of 1, and a minimum value of -1.
How do you know if a point is a maximum or a minimum?
Usually at the minimum or maximum of a function, one of the following conditions arises:The derivative is zero.The derivative is undefined.The point is at the end-points of the domain that is being considered (or of the naturally-defined domain, for example, zero for the square root).This will give you "candidate points"; to find out whether each of these candidate points actually is a maximum or a minimum, additional analysis is required. For example, if the second derivative is positive, you have a minimum, if the second derivative is negative, you have a maximum - but if it is zero, it may be a maximum, a minimum, or neither.
How is the Degree of a polynomial function related to range?
If the domain is infinite, any polynomial of odd degree has infinite range whereas a polynomial of even degree has a semi-infinite range. Semi-infinite means that either the range has a real minimum but no maximum (ie maximum = +infinity) or that it has a real maximum but no minimum (ie minimum = -infinity).
What is the maximum or minimum point called?
A maximum or minimum is generally referred to as an extrema.
How do you determine wheather a quadratic function has a maximum or minimum and how do you find it?
In theory you can go down the differentiation route but because it is a quadratic, there is a simpler solution. The general form of a quadratic equation is y = ax2 + bx + c If a > 0 then the quadratic has a minimum If a < 0 then the quadratic has a maximum [and if a = 0 it is not a quadratic!] The maximum or minimum is attained when x = -b/2a and you evaluate y = ax2 + bx + c at this value of x to find the maximum or minimum value of the quadratic.
