Question

If f(1) = 0 and /"(0) = 1 then f has a local minimum at z = 0. 

          If f(1) = 0 and /"(0) = 1 then f has a local minimum at z = 0.

Added by -Scar B.

Calculus: Early Transcendentals
Calculus: Early Transcendentals
James Stewart 8th Edition
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If f(1) = 0 and /"(0) = 1 then f has a local minimum at z = 0.
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Transcript

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00:01 Hello students, this statement is known as the first derivative test.
00:09 If f dash c is equal to zero then f has a local maximum or minimum at c.
00:14 It's the first derivative test which is useful tool for determining whether a critical point of a function is local maximum or local minimum.
00:23 If f double dash f dash c, f dash c equal to zero and f double dash c is less than zero then f has a local maximum at c.
00:53 If f dash c equal to zero and f double dash c is greater than zero then f has a local minimum at c.
01:17 If f dash c equal to zero and f double dash c equal to zero then the first derivative test is inconclusive and we need to use other methods such as second derivative test or higher order derivative test...
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