Answer:
The correct option is B.
Step-by-step explanation:
The given function is
![f(x)=x^3](https://tex.z-dn.net/?f=f%28x%29%3Dx%5E3)
The translation of a function is defined as
![g(x)=f(x+a)+b](https://tex.z-dn.net/?f=g%28x%29%3Df%28x%2Ba%29%2Bb)
If a>0, then the graph of f(x) shift a units left and if a<0, then the graph of f(x) shift a units right.
If b>0, then the graph of f(x) shift b units up and if b<0, then the graph of f(x) shift b units down.
It is given that the graph of f(x) shifts 4 units left and 2 units down. So, a=4 and b=-2.
![g(x)=f(x+4)+(-2)](https://tex.z-dn.net/?f=g%28x%29%3Df%28x%2B4%29%2B%28-2%29)
![[\because f(x)=x^3]](https://tex.z-dn.net/?f=%5B%5Cbecause%20f%28x%29%3Dx%5E3%5D)
![y=(x+4)^3-2](https://tex.z-dn.net/?f=y%3D%28x%2B4%29%5E3-2)
Therefore option B is correct.
The lowest number is 3.
3 x 588 = 1,764
1,764 = (42) squared
I don't know an easy way to do it. I just slogged through it one-by-one ...
I tried 2 , then I tried 3 and I didn't have to go any farther.
You could have done the same thing. The difference between us is that
I'm willing to work on it just for fun, whereas you're not willing to work on it
even for homework. That's why I became good in math and you might not.
Hi there!
A.) Begin by verifying that both endpoints have the same y-value:
g(-1) = 2(-1)² - 4(-1) + 3
Simplify:
g(-1) = 2 + 4 + 3 = 9
g(2) = 2(2)² - 4(2) + 3 = 8 - 8 + 3 = 3
Since the endpoints are not the same, Rolle's theorem does NOT apply.
B.)
Begin by ensuring that the function is continuous.
The function is a polynomial, so it satisfies the conditions of the function being BOTH continuous and differentiable on the given interval (All x-values do as well in this instance). We can proceed to find the values that satisfy the MVT:
![f'(c) = \frac{f(a)-f(b)}{a-b}](https://tex.z-dn.net/?f=f%27%28c%29%20%3D%20%5Cfrac%7Bf%28a%29-f%28b%29%7D%7Ba-b%7D)
Begin by finding the average rate of change over the interval:
![\frac{g(2) - g(-1)}{2-(-1)} = \frac{3 - 9 }{2-(-1)} = \frac{-6}{3} = -2](https://tex.z-dn.net/?f=%5Cfrac%7Bg%282%29%20-%20g%28-1%29%7D%7B2-%28-1%29%7D%20%3D%20%5Cfrac%7B3%20-%209%20%7D%7B2-%28-1%29%7D%20%3D%20%5Cfrac%7B-6%7D%7B3%7D%20%3D%20-2)
Now, Find the derivative of the function:
g(x) = 2x² - 4x + 3
Apply power rule:
g'(x) = 4x - 4
Find the x value in which the derivative equals the AROC:
4x - 4 = -2
Add 4 to both sides:
4x = 2
Divide both sides by 4:
x = 1/2