Hey there!
It's been a while, hope all has been well!
It's Thanksgiving tomorrow, and I'm thankful for passing this class and feeling okay with all the material we've learned so far. I was very stressed with this class and felt very stupid at times, but hard work allowed me to receive a good grade and feel comfortable with teaching others the material we learned.
We started this trimester with optimization, trying to find dimensions with the given numbers to find the smallest area or the largest area.
Strategy for Solving Max-Min Problems
1. Understand the problem
2. Develop a mathematical model of the problem
3. Graph the function
4. Identify the critical points and endpoints
5. Solve the mathematical model
6. Interpret the Solution
ex) The height of the box is x, and the other two dimensions are (20-2x) and (25-2x). Thus, the volume of the box is
V(x)= x(20-2x)(25-2x)
Expanding, we get
V(x)= 4x^3 - 90x + 500x
the first derivative is
V'(x)= 12x^2 - 180x +500
It's been a while, hope all has been well!
It's Thanksgiving tomorrow, and I'm thankful for passing this class and feeling okay with all the material we've learned so far. I was very stressed with this class and felt very stupid at times, but hard work allowed me to receive a good grade and feel comfortable with teaching others the material we learned.
We started this trimester with optimization, trying to find dimensions with the given numbers to find the smallest area or the largest area.
Strategy for Solving Max-Min Problems
1. Understand the problem
2. Develop a mathematical model of the problem
3. Graph the function
4. Identify the critical points and endpoints
5. Solve the mathematical model
6. Interpret the Solution
ex) The height of the box is x, and the other two dimensions are (20-2x) and (25-2x). Thus, the volume of the box is
V(x)= x(20-2x)(25-2x)
Expanding, we get
V(x)= 4x^3 - 90x + 500x
the first derivative is
V'(x)= 12x^2 - 180x +500
Only c1 is in the domain [0,10] of V.
Critical point value = 820.53
Endpoint values V(0)=0 V(10)=0
Cutout squares that are about 3.68 in. on a side give the maximum volume, about 820.53 in^3.
Critical point value = 820.53
Endpoint values V(0)=0 V(10)=0
Cutout squares that are about 3.68 in. on a side give the maximum volume, about 820.53 in^3.
Another example in this chapter if minimizing the average cost:
The production level (if any) at which average cost is smallest is a level at which the average cost equals the marginal cost.
The production level (if any) at which average cost is smallest is a level at which the average cost equals the marginal cost.
The maximum profit occurs at a production level at which marginal revenue equals marginal cost.