105 =4x
—— —- x=26.25
4. = 4
L'Shonda purchased a container of juice. 80 calories are from carbohydrates.
<u>Solution:</u>
Given that, LShonda purchased a container of juice that contains 200 calories.
The label says that 40% of the calories are from carbohydrates.
We have to find how many calories are from carbohydrates?
Now, according to the given information,
<em>Number of calories from carbohydrates = 40% of the total calories of the juice
</em>
Then, calories from carbohydrates = 40% of 200 calories
40% can be written in fraction as 
Hence, 80 calories are from carbohydrates.
1. Find the derivative of <span>P(x)=3x^3+2x^2-6x. It's P'(x)=9x^2 + 4x - 6.
2. Set this result equal to zero and solve for the critical values:
</span> 9x^2 + 4x - 6 = 0 Using the quadratic formula, I got
x = [-4 plus or minus sqrt(232)] / 18. Reducing this,
x = [-4 plus or minus 2 sqrt(58)]; thus, there are two real, unequal roots and two real, unequal critical values.
3. One at a time, examine the two critical values: determine whether the derivative changes from neg to pos or from pos to neg at each of these values. Example: If the derivative is pos to the left of the first c. v. and neg to the right, we've got a local max.
4. Since there are only 2 critical values, you can have no more than 1 local max (corresponding to a change in the sign of the derivative from pos to neg) and one local min. (from neg to pos).
Message me if this explanation is not sufficient to help you understand this problem thoroughly.
