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# The Second Derivative Test

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The Second Derivative Test
1. The Second-Derivative Test
Let f be a function that is twice differentiable near x
1
and also near x
2
. See Fig. 1. Suppose f '(x
1
)
= 0
and f ''(x
1
) > 0. So the graph of f has a horizontal tangent at x
1
and is concave up there. This
means
that f(x
1
) is a local minimum of f. Similarly, if f '(x
2
) = 0 a..

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