did you check your endpoints?
Post on 14-Feb-2016
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Did you Check your Endpoints?
1st & 2nd Derivative TestsToday you will apply and
formally define the first and second derivative tests.
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Discussion
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1st Derivative Test
Let be a critical number of a function, that is continuous on an open interval containing . If is differentiable on the interval, except possibly at , then( ) can be classified as follows:
1.
c fI c f cf c
If '( ) changes from negative to positive at , then ( ) is a min of .2. If '( ) changes from positive to negative at , then ( ) is a max of .3. If '( ) does not cha
f x c f c relative imum ff x c f c relative imum ff x nge sign at , then ( ) is neither a relative minimum nor a
relative maximum.c f c
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2nd Derivative TestLet be a function such that '( ) 0 and the second derivative of exists on an open intervalcontaining .
1. If "( ) 0, then ( ) is a relative minimum.2. If "( ) 0, then ( ) is a relative maximu
f f cf
c
f c f cf c f c
m.
If "( ) 0, the test fails. In such cases, you can use the 1st derivative test. f c
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Solving Extrema Problems• Identify the quantity to maximize or minimize
and formulate a function in terms of one variable.
• Set the derivative equal to 0 to find the critical numbers. Be sure to look for x-values where the derivative does not exist since critical numbers may occur at those places.
• Use either the first or second derivative test for extrema and be sure to check the endpoints.
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Assignment
HW Q
Have a nice weekend!
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