Answer:
The question is incomplete, the complete question will be:
Suppose you are offered the opportunity to roll a six-sided die, whose faces are 1, 2, 3, 4, 5, and 6. You have no reason to believe one face is any more likely that another. After the roll, you will be paid $1 times and you have the option to throw a die up to three times. You will earn the face value of the die. You have the option to stop after each throw and walk away with the money earned. The earnings are not additive. What is the expected payoff of this game?
Step-by-step explanation:
GCF = -c^2d^3
Factors are -c^2d^3(8c^3d^3 + 27c^2d + 24)
Answer:
6x3+5=23
Step-by-step explanation:
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