4. The Daytona 500 is a NASCAR event that requires drivers to complete 200 grueling laps around a track. Each lap is 2.5 miles. One particular NASCAR driver drove the first 65 laps of the race at a constant speed. The next 65 laps the driver increased their average speed 10mph. For the remaining 70 laps the NASCAR driver increased their average speed an additional 3mph. The driver's total driving time (not including pit stops, etc.) was 2.5 hours. Determine the drivers speed during each stage. Use the table below to help you answer this question Distance (mi) Speed (mph) Stage 1: First 65 Laps Stage 2: Next 65 Laps Stage 3: Last 70 Laps Time (h) 15
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.
For stage 3 in the question, it says that the driver increased their average speed an additional 3mph. Is the right expression 2.5/x+13 or 2.5/x+3 ?
Am I supposed to add the 3 to the previous 10 mph added in Stage 2, or is it a separate case, therefore it's only x+3?
Thank you in advance :)
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