Which expression can be used to determine the skip of the linear function represented in the table
2 answers:
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Answer:
The local maximum and minimum values are:
Local maximum
Local minima
Step-by-step explanation:
Let be . The determination of maxima and minima is done by using the First and Second Derivatives of the Function (First and Second Derivative Tests). First, the function can be rewritten algebraically as follows:
Then, first and second derivatives of the function are, respectively:
First derivative
Second derivative
Now, let equalize the first derivative to solve and solve the resulting equation:
The second-order polynomial is now transform into a product of binomials with the help of factorization methods or by General Quadratic Formula. That is:
The critical points are 0, 5.118 and -1.368.
Each critical point is evaluated at the second derivative expression:
x = 0
This value leads to a local maximum.
x = 5.118
This value leads to a local minimum.
x = -1.368
This value leads to a local minimum.
Therefore, the local maximum and minimum values are:
Local maximum
Local minima