Suppose that a company's monthly profit depends on the number of units sold that month according to theformulaP = – 0.1x + 200x – 100 dollars,%3Dwhere x is the number of units sold.The relationship between how fast monthly profit is changing and how fast monthly sales are changing can bedxwhere f(x) =dtdPwritten in the form= f(x)-dtIf the current monthly sales are 100 units per month and increasing by 2 units per month, is the monthly profitincreasing or decreasing?DecreasingIncreasingIf monthly sales are currently 100 units and increasing by 2 units per month, how fast is the monthly profitchanging?dollars per month

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Suppose that a company's monthly profit depends on the number of units sold that month according to the formula P = - 0.12 + 200x 100 dollars, where z is the number of units sold. The relationship between how fast monthly profit is changing and how fast monthly sales are changing can be dP dx = f(x) dt where f(x) = dt written in the form If the current monthly sales are 100 units per month and increasing by 2 units per month, is the monthly profit increasing or decreasing? Decreasing O Increasing If monthly sales are currently 100 units and increasing by 2 units per month, how fast is the monthly profit changing? dollars per month

Suppose that a company's monthly profit depends on the number of units sold that month according to the formula P = - 0.12 + 200x 100 dollars, where z is the number of units sold. The relationship between how fast monthly profit is changing and how fast monthly sales are changing can be dP dx = f(x) dt where f(x) = dt written in the form If the current monthly sales are 100 units per month and increasing by 2 units per month, is the monthly profit increasing or decreasing? Decreasing O Increasing If monthly sales are currently 100 units and increasing by 2 units per month, how fast is the monthly profit changing? dollars per month

Trigonometry (11th Edition)

11th Edition

ISBN:9780134217437

Author:Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels

Publisher:Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels

Chapter1: Trigonometric Functions

Section: Chapter Questions

Problem 1RE: 1. Give the measures of the complement and the supplement of an angle measuring 35°.

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Concept explainers

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.

Question

Suppose that a company's monthly profit depends on the number of units sold that month according to the
formula
P = – 0.1x + 200x – 100 dollars,
%3D
where x is the number of units sold.
The relationship between how fast monthly profit is changing and how fast monthly sales are changing can be
dx
where f(x) =
dt
dP
written in the form
= f(x)-
dt
If the current monthly sales are 100 units per month and increasing by 2 units per month, is the monthly profit
increasing or decreasing?
Decreasing
Increasing
If monthly sales are currently 100 units and increasing by 2 units per month, how fast is the monthly profit
changing?
dollars per month

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