33b 5 Consider the function For this function there are thre

3-3b #5

Consider the function $\"f(x)$ . For this function there are three important intervals: $\"(-\\infty,$ , $\"[A,B]\"$ , and $\"[B,\\infty)\"$ where $\"A\"$ and $\"B\"$ are the critical numbers.
Find $\"A\"$
and $\"B\"$
For each of the following intervals, tell whether $\"f(x)\"$ is increasing (type in INC) or decreasing (type in DEC).
$\"(-\\infty,$ :
$\"[A,B]\"$ :
$\"[B,\\infty)\"$ :

$\"f(x)\"$ has an inflection point at $\"x$
where $\"C\"$ is
For each of the following intervals, tell whether $\"f(x)\"$ is concave up (type in CU) or concave down (type in CD).
$\"(-\\infty,$ :
$\"(C,\\infty)\"$ :

f\'(x)= -6x^2 +54 x -84 Set equal to 0 -6x^2 +54x-84=0 x^2 -9x +14=0 (x-7)(x-2)=0 x=7,2 A=2 B=7 From negative infinity to 2 f\'(x)<0 so the function is decreasing From 2 to 7 the function is increasing From 7 to positive infinity the function is decreasing f\'\'(x)= -12x +54 -12x +54=0 x= -54/-12= 9/2 Inflection point at x=9/2 From neg infinity to 9/2 function is concave up (second derivative is positive) From 9/2 to pos infinity the function is concave down.(second derivative is negative).

3-3b #5 Consider the function. For this function there are three important intervals:,, andwhereandare the critical numbers. Find and For each of the following

33b 5 Consider the function For this function there are thre

Solution

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