+0  
 
0
51
5
avatar+702 

http://prntscr.com/lisuzo

critical  Nov 15, 2018
 #1
avatar+422 
0

a) We must let \(f(x)=0\).

\(3x^3+10x^2-13x-20=0\), and solving we get \(x=-4, -1, \frac{5}{3}\) .

Therefore, the x-intercepts are \(x=-4, -1, \frac{5}{3}\).

 

b) Let \(x=0\) , and solving we get \(-20\) .

Therefore, the y-intercept is \(y=-20\).

 

c) This is simple, make a point between \(x=-4\) and \(x=-1\), for example, \((-3, 0)\).

Same for \(x=-1\) and \(x=5/3\) , for example, \((1, 0)\) .

 

d) As \(x\) goes toward negative infinity, we know that \(x^3\) will always decrease, and vice versa.

 

e) Your graph may look something like this:

 

You are very welcome!

:P

CoolStuffYT  Nov 15, 2018
 #2
avatar+702 
0

!!! :)

critical  Nov 15, 2018
 #3
avatar+92785 
+1

 

Let's see how CS  might have determined the x intercepts  (roots)

 

3x^3 + 10x^2 -13x - 20

 

By the Rational Roots Theorem ......one possible root is  -1

So

3(-1)^3 + 10(-1)^2 - 13(-1) - 20 =  -3 + 10 + 13 - 20  =  0

 

Using synthetic division, we can find the remaining polynomial

 

 

-1  [  3   10    - 13     -20 ]

              -3     - 7       20

      __________________

       3     7    -20         0

 

 

So....the remaining polynomial is   3x^2  + 7x - 20

 

Factoring, we have

 

(3x - 5) ( x + 4)

 

Setting each factor to 0  and solving for x we have that the other two roots are

x= 5/3     and x = -4

 

Then the x intercepts are  x = -4, -1   and 5/3

 

The rest of the answer is as CS has shown....!!!

 

 

cool cool cool

CPhill  Nov 15, 2018
 #4
avatar+702 
0

thankyouu bothh

critical  Nov 15, 2018
 #5
avatar+422 
0

You're welcome! ;)

CoolStuffYT  Nov 15, 2018

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