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7. (10) Let U CR” be open, c EU, f:U + R, and suppose f'(c; u) exists for all u ER". Show that either f'(c; u) = 0 for a

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7 10 Let U Cr Be Open C Eu F U R And Suppose F C U Exists For All U Er Show That Either F C U 0 For A 1
7 10 Let U Cr Be Open C Eu F U R And Suppose F C U Exists For All U Er Show That Either F C U 0 For A 1 (31.31 KiB) Viewed 29 times
7. (10) Let U CR” be open, c EU, f:U + R, and suppose f'(c; u) exists for all u ER". Show that either f'(c; u) = 0 for all u € R" or 3u1, U2 E R" such that f'(c; u1) > 0 and f'(c; u2) <0.