The university theatre department is selling tickets to their
1 answer:
You might be interested in
Answer:
The zeros of the given polynomial function f(x) are -3,0,-4
Step-by-step explanation:
Given polynomial is
To find the zeros of the given polynomial:
First equate the polynomial function f(x) to zero
That is
By synthetic division we can solve it
-3_| 3 21 36 0
0 -9 -36 0
_____________________
3 12 0 0
Therefore x+3 is a factor
That is x=-3 is a zero
3x=0 or x+4=0
Therefore x=0 or x=-4
Therefore the zeros are -3,0,-4
9514 1404 393
Answer:
- relative minimum -6√3 at x = -√3
- relative maximum 6√3 at x = √3
- decreasing on x < -√3 and x > √3
- increasing on -√3 < x < √3
- see below for a graph
Step-by-step explanation:
I find it convenient to draw the graph first when looking for relative extrema.
The function can be differentiated to get ...
f'(x) = -3x^2 +9
This is zero when ...
-3x^2 +9 = 0
x^2 = 3
x = ±√3 . . . . . x-values of relative extrema
Then the extreme values are ...
f(±√3) = x(9 -x^2) = (±√3)(9 -3) = ±6√3
The lower extreme (minimum) corresponds to the lower value of x (-√3), so the extrema are ...
(x, y) = (-√3, -6√3) and (√3, 6√3)
__
Since the leading coefficient is negative and the degree is odd, the function is decreasing for values of x below the minimum and above the maximum. It is increasing for values of x between the minimum and the maximum.
decreasing: x < -√3, and √3 < x
increasing: -√3 < x < √3
