We want to find the value of n that will maximize the function An = 11n - n^2.
To find the maximum value, we need to find the critical points of the function by taking the derivative of An with respect to n and setting it equal to 0.
An = 11n - n^2 An' = 11 - 2n
Setting An' equal to 0 to find the critical point: 11 - 2n = 0 2n = 11 n = 5.5
Therefore, the critical point occurs at n = 5.5.
To determine if this critical point is a maximum or minimum, we can check the second derivative: An'' = -2 (which is negative)
Since the second derivative is negative, the critical point n = 5.5 corresponds to a maximum value of the function.
We want to find the value of n that will maximize the function An = 11n - n^2.
To find the maximum value, we need to find the critical points of the function by taking the derivative of An with respect to n and setting it equal to 0.
An = 11n - n^2
An' = 11 - 2n
Setting An' equal to 0 to find the critical point:
11 - 2n = 0
2n = 11
n = 5.5
Therefore, the critical point occurs at n = 5.5.
To determine if this critical point is a maximum or minimum, we can check the second derivative:
An'' = -2 (which is negative)
Since the second derivative is negative, the critical point n = 5.5 corresponds to a maximum value of the function.