The management of Ditton Industries has determined that the daily marginal revenue function associated with selling x units of their deluxe toaster ovens is given by the following, where R '(x) is measured in dollars/unit.R'(x) = -0.1x + 40(a) Find the daily total revenue realized from the sale of 220 units of the toaster oven.$ (b) Find the additional revenue realized when the production (and sales) level is increased from 220 to 320 units.$

Q: Suppose the supply of x units of a product at price p dollars per unit is given by p = 20 + 40…

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Q: e marginal profit for a certain style of hiking boots is given by P'(x) = 45 - 0.83x dollars per…

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Q: Find Cost Function 314+4 C'(x)=x+4 $ 81 units

A: Given, C'(x) = x34 + 4  and cost of 81 units is  1629

Q: The revenue (in thousands of dollars) from producing x units of an item is modeled by…

A: The revenue  function is

Q: If a population of bacteria is modeled by the equation p(t) = te^−t^2 million bacteria, with t in…

A: Given, Population of bacteria is modeled by the equation, pt = te-t2  million bacteria When the rate…

Q: Suppose that the demand for x units of a product is x = 9,000 – 90p where p dollars is the price per…

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Q: (c) C'(x) = 5x - ; 10 units cost at $94.20

A:

Q: Find y''' for y = 1/(x+4)3

A: To find the first derivative, y' of y, differentiate (x+4)-3 with respect to x, using the general…

Q: A company estimates that it will sell N(x) units of a product after spending Sx thousand on…

A:

Q: Suppose a company's profit (in dollars) is given by P(x) = 270x - 0.3x² - 5,300, where x is the…

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Q: Find g'(x) if g(x) %3D Зx е бх

A: Product rule of the derivative is, (uv)’=u’v+uv’ where u and v are the functions of x.

Q: f(x) = xV 3 - x² — х

A: Solution: The objective is to find the derivative of the given function

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.