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October 6th, 2012, 03:30 PM   #1
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1st derivative test

For the following function, fill in the table to find where the function is increasing or decreasing.

y = f(x) = x^(2) + 6x + 10
f ' (x) = 2x + 6

open interval -infinity<x<0 0<x<+infinity

Test # -2 1

sign of f '(x) increasing increasing

conclusion ? ?


minimum occurs at ? is it -3 ?

Thanks for any and all help
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October 6th, 2012, 05:41 PM   #2
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Re: 1st derivative test

Quote:
Originally Posted by mathkid
y = f(x) = x^(2) + 6x + 10
f ' (x) = 2x + 6
Correct. So, we do

2x + 6 = 0

2x = -6

x = -6/2 = -3.

Note that f(x) is a parabola, so there is one (global) extremum, a minimum at x = -3, y = 1.

Good work.
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October 6th, 2012, 06:29 PM   #3
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Re: 1st derivative test

Thanks Greg
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October 6th, 2012, 06:30 PM   #4
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Re: 1st derivative test

To determine the intervals on which the function is increasing/decreasing, you first find the critical number(s). For this function this is

This gives you the two intervals:

i)

Test value

function decreasing on this interval.

ii)

Test value

function increasing on this interval.

So, we can therefore conclude that the function has a relative (in this case a global) minimum at .
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October 6th, 2012, 07:14 PM   #5
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Re: 1st derivative test

I got it right Mark. Need help on other question finding critical value(s).
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October 6th, 2012, 07:22 PM   #6
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Re: 1st derivative test

You gave different intervals...I just wanted to demonstrate the method I was taught to use.
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