+1252 a) We must let f(x)=0.
3x3+10x2−13x−20=0, and solving we get x=−4,−1,53 .
Therefore, the x-intercepts are x=−4,−1,53.
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 x3 will always decrease, and vice versa.
e) Your graph may look something like this:
You are very welcome!
:P
+130474
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....!!!
