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What is the range of a a function f when it is defined by f x 2 cos 3 x where x is a real number?
f(x) = 2 cos 3x The amplitude: A = |2| = 2 The maximum value of the function: 2 The minimum value of the function: -2 The range: [-2, 2]
How do you know if a graph is a function?
A graph is a function if there is no more than one y-value for any x value. This means no vertical lines or "C" shapes, etc
What is the maximum and minimum of quadratic function parent function?
The minimum is the vertex which in this case is 0,0 or the origin. There isn't a maximum.....
How will you describe the graph of a function?
· whether it is linear, quadratic or exponential · whether it has an upper or lower bound · whether it has a minimum or a maximum value · whether it is constant, decreasing or increasing
A value is in the domain of a function if there is an on the graph of the function at that x-value?
point
What is the definition of the Minimum of a function in Alegbra?
A global minimum is a point where the function has its lowest value - nowhere else does the function have a lower value. A local minimum is a point where the function has its lowest value for a certain surrounding - no nearby points have a lower value.
What is the minimum value that cosecant can be of an angle?
There is no minimum value for the cosecant function.
How do you find minimum and maximum value of calculus?
For the function y = x^(3) + 6x^(2) + 9x Then dy/dx = 3x^(2) + 12x + 9 At max/min dy/dx = 0 Hence 3x^(2) + 12x + 9 = 0 3(x^(2) + 4x + 3) = 0 Factor (x + 1)(x + 3) = 0 Hence x = -1 & x = -3 are the turning point (max/min) To determine if x = 0 at a max/min , the differentiate a second time Hence d2y/dx2 = 6x + 12 = 0 Are the max/min turning points. Substitute , when x = -1 6(-1) + 12 = (+)6 minimum turning point . x = -3 6(-3) + 12 = -6 maximum turning point. When x = positive(+), then the curve is at a minimum. When x = negative (-), then the curve is at a maximum turning point. NB When d2y/dx2 = 0 is the 'point of inflexion' , where the curve goes from becoming steeper/shallower to shallower/steeper. So when d2y/dx2 = 6x + 12 = 0 Then 6x = -12 x = -2 is the point of inflexion. NNB When differentiating the differential answer gives the steeper of the gradient. So if you make the gradient zero ( dy/dx = 0) , there is no steepness, it is a flat horizontal line
What is the minimum value of the cube root parent function?
The global minimum value is always negative infinity.
What is the minimum value that the function y equals cos x assumes?
Since the range of the cosine function is (-1,1), the function y = cos(x) assumes a minimum value of -1 for y.
What is The sum of maximum value of sin and minimum value of cos?
The maximum value of the sine function, (\sin(x)), is 1, while the minimum value of the cosine function, (\cos(x)), is -1. Therefore, the sum of the maximum value of sine and the minimum value of cosine is (1 + (-1) = 0).
What is the vertex of the quadratic function?
It if the max or minimum value.
How can you use the zeros of a function to find the maximum or minimum value of the function?
You cannot. The function f(x) = x2 + 1 has no real zeros. But it does have a minimum.
What is an extreme value in a set?
the maximum or minimum value of a continuous function on a set.
What is the minimum value of the function u(x, y) when considering both x and y as variables?
The minimum value of the function u(x, y) occurs at the point where the function reaches its lowest value when both x and y are considered as variables.
Is a relative minimum also an absolute minimum?
A relative minimum is a point where a function's value is lower than that of its immediate neighbors, but it is not necessarily the lowest value over the entire domain. An absolute minimum, on the other hand, is the lowest value of the function across its entire range. Therefore, while a relative minimum can be an absolute minimum if it is the lowest point overall, they are not the same and one does not imply the other.
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.
