In a tidal river, the time between high and low tide is 5.8 hours. At high tide the depth of water is 17.7 feet, while at low tide the depth is 4.1 feet. Assume the water depth as a function of time can be expressed by a trigonometric function (sine or cosine). (a) Graph the depth of water over time if there is a high tide at 12:00 noon. Label your graph indicating low and high tide. Select the letter of the graph which best matches your graph. Assume that t = 0 is noon. Choose v A B (b) Write an equation for the depth f(t) of the tide (in feet) t hours after 12:00 noon. f(t) = help (formulas) (C) A boat requires a depth of 8 feet to set sail, and is docked at 12:00 noon. What is the latest time in the afternoon it can set sail? Round your answer to the nearest minute. For example, if you find f(t) = 8 when t = 1.25, you would answer at 1:15 PM (since this is 1 and a quarter hours after noon). D The latest the boat can leave is at PM
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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