It has an absolute minimum at the point (2,3). It has no maximum but the ends of the graph both approach infinity.
If x is the unknown or variable in an equation it can have many possible maximum or minimum values
When the quadratic is written in the form: y = ax2 + bx + c then if a > 0 y has a minimum if a < 0 y has a maximum and if a = 0 y is not a quadratic but y = bx + c, and it is linear. The maximum or minimum is at x = -b/(2a)
A maximum!A maximum!A maximum!A maximum!
There is no maximum but te minimum is 15.
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.
It has an absolute minimum at the point (2,3). It has no maximum but the ends of the graph both approach infinity.
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.
Both the function "cos x" and the function "sin x" have a maximum value of 1, and a minimum value of -1.
Sin(x) has a maximum value of +1 and a minimum value of -1.
If x is the unknown or variable in an equation it can have many possible maximum or minimum values
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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.
You cannot. The function f(x) = x2 + 1 has no real zeros. But it does have a minimum.
When the quadratic is written in the form: y = ax2 + bx + c then if a > 0 y has a minimum if a < 0 y has a maximum and if a = 0 y is not a quadratic but y = bx + c, and it is linear. The maximum or minimum is at x = -b/(2a)
(x-2) is not a factor of the numerator and so y tends to minus infinity as x approaches 2 from below. As x approaches 2 from above, y tends to plus infinity. There are, therefore, no maximum or minimum values for y.
A maximum!A maximum!A maximum!A maximum!