Question
Consider and the closed circular region
Find points in R where |
| has its maximum and minimum values.
Answer :
Word Count : 333
We need to find the maximum and minimum values of \( |f(z)| \) for the function: \[ f(z) = z^2 - z \] on the closed circular region: \[ R = \{z : |z| \leq 1\} \] ### Step 1: Evaluating \( |f(z)| \) at Critical Points Inside \( R \) To find the critical points, we differentiate \( f(z) \): \[ f'(z) = 2z - ______ ______ _______ ____ ___ ______ ____ ____ ________ ______ __________.
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We need to find the maximum and minimum values of \( |f(z)| \) for the function: \[ f(z) = z^2 - z \] on the closed circular region: \[ R = \{z : |z| \leq 1\} \] ### Step 1: Evaluating \( |f(z)| \) at Critical Points Inside \( R \) To find the critical points, we differentiate \( f(z) \): \[ f'(z) = 2z - ______ ______ _______ ____ ___ ______ ____ ____ ________ ______ __________.
____ ________ _________ ______ __________ _______ __________ _________.
___ ___ ____ _______ ________ _______ __________ ___.
___ _______ ________ _____ ______ ______.
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| has its maximum and minimum values.
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