![y=x^5-3\\ y'=5x^4\\\\ 5x^4=0\\ x=0\\ 0\in [-2,1]\\\\ y''=20x^3\\\\ y''(0)=20\cdot0^3=0](https://tex.z-dn.net/?f=y%3Dx%5E5-3%5C%5C%20y%27%3D5x%5E4%5C%5C%5C%5C%205x%5E4%3D0%5C%5C%20x%3D0%5C%5C%200%5Cin%20%5B-2%2C1%5D%5C%5C%5C%5C%20y%27%27%3D20x%5E3%5C%5C%5C%5C%0Ay%27%27%280%29%3D20%5Ccdot0%5E3%3D0)
The value of the second derivative for

is neither positive nor negative, so you can't tell whether this point is a minimum or a maximum. You need to check the values of the first derivative around the point.
But the value of

is always positive for

. That means at

there's neither minimum nor maximum.
The maximum must be then at either of the endpoints of the interval
![[-2,1]](https://tex.z-dn.net/?f=%5B-2%2C1%5D)
.
The function

is increasing in its entire domain, so the maximum value is at the right endpoint of the interval.
The pair of equations:
y = x + 4
y = -2x - 2
To solve the system of equation by substitution, you would substitute one variable for it's equivalent expression. Combining the pair of equations into one equation in only one variable. The easiest way to do this is by substituting out the variable y because it is already alone on one side of the equal sign. Substitute the y in the second equation for: x+4
x+4 = -2x - 2
solve for x
x + 2x = -2 -4
3x = -6
x = -2
now use the value for x to find y by putting into either equation.
y = x + 4
y = (-2) + 4
y = 2
solution is: (-2, 2)
Answer:
The critical value that should be used in constructing the interval is T = 5.8408.
The 99% confidence interval for the true mean yield is between 2.943 bushels per acre and 96.268 bushels per acre.
Step-by-step explanation:
We have the standard deviation of the sample, so we use the students t-distribution to solve this question.
The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So
df = 4 - 1 = 3
99% confidence interval
Now, we have to find a value of T, which is found looking at the t table, with 3 degrees of freedom(y-axis) and a confidence level of
. So we have T = 5.8408. This is the critical value.
The margin of error is:
M = T*s = 5.8408*7.99 = 46.668 bushels per acre
In which s is the standard deviation of the sample.
The lower end of the interval is the sample mean subtracted by M. So it is 49.6 - 46.668 = 2.943 bushels per acre.
The upper end of the interval is the sample mean added to M. So it is 49.6 + 46.668 = 96.268 bushels per acre.
The 99% confidence interval for the true mean yield is between 2.943 bushels per acre and 96.268 bushels per acre.