Outside temperature over a day can be modeled as a sinusoidal function. Suppose you know the temperature varies between 47 and 83 degrees during the day and the average daily temperature first occurs at 9 AM. How many hours after midnight, to two decimal places, does the temperature first reach 56 degrees?

Q: Outside temperatures over a 24-hour period can be modeled by a sinusoidal function. Suppose the high…

A: Given: The outside temperature over a 24hours is modeled using a sinusoidal function. The high…

Q: Below is the graph of the heights reached by the cars of the Thunderoll Roller Coaster over its…

A: Topic - Average rate of change of function. We are given graph of a function,we know the points on…

Q: Explain finding the period of a trig function (including tan, cot, sec, and csc) and provide example…

A: We have to explain how to find the period of a trig function (including tan, cot, sec, and csc) and…

Q: The function models variation in body temperature, y, in °F, x hours after midnight. a. What is body…

A: Consider the given equation: y=98.6+0.3sinπ12x-11π12 Where The function models variation in body…

Q: What is the period of a function?

A: Period of the function: The function f is said to periodic function if there exist P in ℝ such that…

Q: The size of a bird population on an island can be described by a sinusoidal graph. The number of…

A:

Q: 1. A student throws a book into the air and records the book's height as a function of time. Time…

A: Time (sec)00.51.01.52.02.53.03.54.04.55.0Height (fr)6.044.575.097.5112.0118.5117107.590.064.531.0

Q: The actual temperature inside an oven varies around the selected temperature. This variation can be…

A:

Q: Outside temperatures over a 24-hour period car be modeled by a sinusoidal function. Suppose the high…

A: Given:Outside temperature over a 24 hour can be modeled by a sinusoidal function.The high…

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.