When a car skids to a stop, the length L, in feet, of the skid marks is related to the speed S, in miles per hour, of the car by the power function below. 30 s2 Here the constant h is the friction coefficient, which depends on the road surface.t For dry concrete pavement, the value of h is about 0.85. (Round your answers to two decimal places.) (a) If a driver going 55 miles per hour on dry concrete jams on the brakes and skids to a stop, how long will the skid marks be? ft (b) A policeman investigating an accident on dry concrete pavement finds skid marks 183 feet long. The speed limit in the area is 70 miles per hour. Is the driver in danger of getting a speeding ticket? The driver's speed was mph so it appears the driver --Select--- v be in danger of getting a ticket. (c) This part of the problem applies to any road surface, so the value of h is not known. Suppose you are driving at 65 miles per hour but, because of approaching darkness, you wish to slow to a speed that will cut your emergency stopping distance in half. What should your new speed be? (Hint: You should use the homogeneity property of power functions here. By what factor should you change your speed to ensure that L changes by a factor of 0.5?) mph
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.
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