The graph shows the megawatts of electricity used on one day in one city. a. Is this the graph of a function? 2200- O No O Yes 1600- 1500- 1400- 1300- 1200- 1100- 1000- b. What is the domain? (Type your answer in interval notation) 12 16 Noon Hours (hr) 20 24 c. Estimate the number of megawatts used at 9 A.M. MW (Round to the nearest MW as needed.) d. At which hour, 0-24, was the most electricity used? Ohr (Round to the nearest hour as needed.) At which hour, 0-24 was the least electricity used? O hr (Round to the nearest hour as needed.) e. Call this function f. What is f(12)? f(12) = MW (Round to the nearest MW as needed.) Megavatts (MW)
Minimization
In mathematics, traditional optimization problems are typically expressed in terms of minimization. When we talk about minimizing or maximizing a function, we refer to the maximum and minimum possible values of that function. This can be expressed in terms of global or local range. The definition of minimization in the thesaurus is the process of reducing something to a small amount, value, or position. Minimization (noun) is an instance of belittling or disparagement.
Maxima and Minima
The extreme points of a function are the maximum and the minimum points of the function. A maximum is attained when the function takes the maximum value and a minimum is attained when the function takes the minimum value.
Derivatives
A derivative means a change. Geometrically it can be represented as a line with some steepness. Imagine climbing a mountain which is very steep and 500 meters high. Is it easier to climb? Definitely not! Suppose walking on the road for 500 meters. Which one would be easier? Walking on the road would be much easier than climbing a mountain.
Concavity
In calculus, concavity is a descriptor of mathematics that tells about the shape of the graph. It is the parameter that helps to estimate the maximum and minimum value of any of the functions and the concave nature using the graphical method. We use the first derivative test and second derivative test to understand the concave behavior of the function.
![**The graph shows the megawatts of electricity used on one day in one city.**
**a. Is this the graph of a function?**
- [ ] No
- [ ] Yes
**b. What is the domain?**
(Type your answer in interval notation)
[ ]
**c. Estimate the number of megawatts used at 9 A.M.**
[ ] MW
(Round to the nearest MW as needed.)
**d. At which hour, 0-24, was the most electricity used?**
[ ] hr
(Round to the nearest hour as needed.)
**e. At which hour, 0-24, was the least electricity used?**
[ ] hr
(Round to the nearest hour as needed.)
**f. Call this function f. What is f(12)?**
f(12) = [ ] MW
(Round to the nearest MW as needed.)
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### Explanation of Graph:
The graph provided illustrates the megawatts of electricity used over a 24-hour period in one city. The x-axis represents the hours of the day (from 0 to 24, with noon marked), and the y-axis represents the electricity usage in megawatts (MW), ranging from 700 MW to 2500 MW.
### Key Observations from the Graph:
1. The electricity usage starts slightly above 900 MW at hour 0.
2. It initially increases, reaching approximately 1400 MW around hour 6.
3. There is a substantial peak in electricity usage, rising to roughly 2400 MW between hours 10 and 12.
4. A steep decline follows, dropping to approximately 800 MW at hour 18.
5. Finally, the usage slightly rises again towards the end of the day but does not exceed 1500 MW.
This graph is useful for understanding the patterns of electricity usage throughout the day and identifying peak usage times for efficient energy management.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ffb04437b-3f7e-4496-ba03-3a7f713d70b1%2F40b157c5-15d5-4eb0-bfa8-a85f42817d59%2Fkvktb1k_processed.png&w=3840&q=75)
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