Answer: 
<u>Simplify both sides of the equation</u>
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<u>Subtract 2 from both sides</u>
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<u>Divide both sides by 2</u>
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![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 distance between any two points is:
d^2=(x2-x1)^2+(y2-y1)^2
d^2=(6--2)^2+(4--4)^2
d^2=8^2+8^2
d^2=64+64
d^2=128
d=√128 units
Answer:
1. Lisa purchased almonds for $3.00 and spent $24.90.
The quantity of almonds bought is therefore:
= Total amount spent / Cost per pound
= 24.90 / 3
= 8.3 pounds
2. If the price goes up to $3.50 per pound and the maximum Lisa can spend is $25, the number of pounds she can get is:
= Maximum amount for almonds / Price per almonds
= 25 / 3.5
= 7.14 pounds
Answer:
Cost of one doughnut = $1.25
Step-by-step explanation:
Doughnut Cost
3 3.75
1 x
