Let A ( x )= x (x+7). Answer the following questions. 1. Find the interval(s) on

ID: 2853888 • Letter: L

Question

Let A(x)=x(x+7). Answer the following questions.

1. Find the interval(s) on which A is increasing.
Answer (in interval notation):

2. Find the interval(s) on which A is decreasing.
Answer (in interval notation):

3. Find the local maxima of A. List your answers as points in the form (a,b).
Answer (separate by commas):

4. Find the local minima of A. List your answers as points in the form (a,b).
Answer (separate by commas):

5. Find the interval(s) on which A is concave upward.
Answer (in interval notation):

6. Find the interval(s) on which A is concave downward.
Answer (in interval notation):

Please show work and/or explain how you got to your answer so that I can have a better understanding. Thanks!

A'(x) = x(x + 7)

If A'(x) > 0, where A(x) is increasing...

=> 3x+14 >0 => 3x >-14 => x> -14/3 so answer i ( -14/3 , inifinity ) for increasing

for decreasing we should have A'(x) < 0 so we get frm above ( - infinity , -14/3 ) ------decreasing

3 &4 . critical point => f dash x=0 => x= -14/3

fdouble dash (x) =

put x= -14/3 = > f double dash =0.98 , which is >0 so it is a point of minima

put x= -14/3 in y , we get -7.12 so point of minimum = (-14/3 , -7.12 ) ------answer 4

we don't have any maxima bcoz the only critical point turned out to be minimum so maximum will be infinity ( infinity , infinity ) -----answer 3

5 & 6 concave up when f double dash (x) >0 and concave down when f double dash <0 . we solved f double dash x above , plz refer

so concave up = (-28/3 , inifinity ) and concave down (-inifinity , -28/3) ------answer 5 &6

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