If a manufacturer charges p(x) dollars per item, where p(x) = 4 – 5, then x thousand items will be sold. (a) Find an expression for the total revenue from the sale of x thousand items. (b) Find the value of x that leads to maximum revenue. (c) Find the maximum revenue.

Q: Find a formula for the exponentail function passing through the points (-2,40) and (1,5)

A: The general equation for an exponential equation is  y = a(b)x

Q: Graph the function f(x) = x-1

A: f(x)=x-1 For x-intercept: f(x)=0 =>x-1=0 =>x=1 For y-intercept: x=0 f(0)=0-1 =>f(0)=-1

Q: Let f(x)=|4+10x|.

A:

Q: From 2005 through 2010, an Internet sales company was hiring new employees at a rate of n(x) = 588 +…

A: We need to find function.

Q: f (x) = x-5>2

A: The given inequality is x-5>2. Solve this inequality as follows.

Q: Is the point (1, -2) on the graph of the function k(x) = x2 + (2>x)?

A: Given, k(x) = x2 + (2/x) To check Is the point (1, -2) on the graph of the function

Q: Identify the vertex of the graph of the function y = 2(x + 1)²-3

A: given  y=2(x+1)2-3 standard form is y=a(x-h)2+k where (h,k)  is vertex

Q: Is f(x) = 2x3 - 5 a one-to-one function?

A: A function f(x) is said to one one if, fx1=fx2⇒x1=x2

Q: Graph the function h (x)=- 2x- 1. 6- 4. 2.

A: The function given above represent a straight line.  First let us discuss the method for plotting  a…

Q: Write a function to model the scenario [y=a (x-h)2 + k]

A: We will find out the required function.

Q: The function T(x)=65x is the number of words, T(x) that a secretary can type in x minutes. How many…

A: Consider the given function as Tx=65x Where Tx that a secretary can type in x minutes.

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.