Hi there!
![\large\boxed{(-\infty, \sqrt[3]{-4}) \text{ and } (0, \infty) }](https://tex.z-dn.net/?f=%5Clarge%5Cboxed%7B%28-%5Cinfty%2C%20%5Csqrt%5B3%5D%7B-4%7D%29%20%5Ctext%7B%20and%20%7D%20%280%2C%20%5Cinfty%29%20%7D)
We can find the values of x for which f(x) is decreasing by finding the derivative of f(x):
Taking the derivative gets:
Find the values for which f'(x) < 0 (less than 0, so f(x) decreasing):
0 = -8/x³ - 2
2 = -8/x³
2x³ = -8
x³ = -4
![x = \sqrt[3]{-4}](https://tex.z-dn.net/?f=x%20%3D%20%5Csqrt%5B3%5D%7B-4%7D)
Another critical point is also where the graph has an asymptote (undefined), so at x = 0.
Plug in points into the equation for f'(x) on both sides of each x value to find the intervals for which the graph is less than 0:
f'(1) = -8/1 - 2 = -10 < 0
f'(-1) = -8/(-1) - 2 = 6 > 0
f'(-2) = -8/-8 - 2 = -1 < 0
Thus, the values of x are:
![(-\infty, \sqrt[3]{-4}) \text{ and } (0, \infty)](https://tex.z-dn.net/?f=%28-%5Cinfty%2C%20%5Csqrt%5B3%5D%7B-4%7D%29%20%5Ctext%7B%20and%20%7D%20%280%2C%20%5Cinfty%29)
Answer:
y = - 16t² + 55.6t + 6
Step-by-step explanation:
Using y - y₀ = vt - 1/2gt² where g = 32 ft/s², and v the velocity of the football
So y = y₀ + vt - 1/2 × (32 ft/s²)t²
y = y₀ + vt - 16t² where y₀ = 6.5 ft
y = 6 + vt - 16t²
Now, when t = 3.5 s, that is the time the teammate catches the ball after the quarterback throws it, y = 5 ft. Substituting these into the equation, we have
5 = 6.5 + v(3.5 s) - 16(3.5 s)²
5 = 6.5 + 3.5v - 196
collecting like terms, we have
5 - 6.5 + 196 = 3.5v
194.5 = 3.5v
v = 194.5/3.5 = 55.57 ft/s ≅ 55.6 ft/s
So, substituting v into y, our quadratic model is
y = 6 + 55.6t - 16t²
re-arranging, we have
y = - 16t² + 55.6t + 6
Answer:
-1
Step-by-step explanation:
The amount of freezers that can be shipped is 70. I'm not completely sure, because I do not know how many pounds the ovens are. But to get the answer, just simply divide 42000 by 600.
Answer:
<h2>VU=16</h2><h2>x=2</h2>
Step-by-step explanation:
lets solve the problem 7x+2=3x+10
subtract 3x from 7x
4x+2=10
subtract 2 from 10
4x=8
divide both sides by 4
x=2
to find VU plug in 2 for x so...
3(2)+10
6+10
16
I hope this helped you :)
