Answer:
max{x²-4x²+5} = 5 at x = 0
Step-by-step explanation:
1. Find the critical numbers by finding the first derivative of f(x), set it to 0 and solve for x.
![f'(x)=0](https://tex.z-dn.net/?f=f%27%28x%29%3D0)
We get:
![f(x) = -3x^2+5\\f'(x) = -6x\\-6x = 0\\x = 0](https://tex.z-dn.net/?f=f%28x%29%20%3D%20-3x%5E2%2B5%5C%5Cf%27%28x%29%20%3D%20-6x%5C%5C-6x%20%3D%200%5C%5Cx%20%3D%200)
So the critical number is x = 0.
2. Evaluate the first derivative by plugging in the critical number and see if the derivative is positive or negative on both sides:
is positive when the x < 0 (for example: -6*(-1)=+)
is negative when the x > 0 (for example: -6*(1)=-)
Therefore, you have a local maximum.
Now just get the Y value by plugging in the critical number in the original function. ![f(0)=5](https://tex.z-dn.net/?f=f%280%29%3D5)
local maximum is (0,5)
Answer:
Step-by-step explanation:
110_5
Answer:
not really sure for number one
1. 1.56y × 3.9x
2. 4.8x + 9.6y
Answer:
D. ![y=-0.927x+13.634](https://tex.z-dn.net/?f=y%3D-0.927x%2B13.634)
Step-by-step explanation:
We graph the points on the graph. The graph is attached.
Let us take two points (1, 14) and (15, 1), and calculate the slope
between them <em>(we choose these points because the line passing through them will be the best fit for all points) </em>
![m=\frac{14-1}{1-15} =\frac{13}{-14} =-0.9286](https://tex.z-dn.net/?f=m%3D%5Cfrac%7B14-1%7D%7B1-15%7D%20%3D%5Cfrac%7B13%7D%7B-14%7D%20%3D-0.9286)
Thus we have the equation
![y=-0.9286x+b](https://tex.z-dn.net/?f=y%3D-0.9286x%2Bb)
Let us now calculate
from the point ![(1,14)](https://tex.z-dn.net/?f=%281%2C14%29)
![14=-0.9286(1)+b](https://tex.z-dn.net/?f=14%3D-0.9286%281%29%2Bb)
![b=14.9286](https://tex.z-dn.net/?f=b%3D14.9286)
So the equation we get is
![y=-0.9286x+14.9286](https://tex.z-dn.net/?f=y%3D-0.9286x%2B14.9286)
Let us now turn to the choices given and see which choice is closest to our equation: we see that choice D.
is the closest one, so we pick it.