The management of ThermoMaster Company, whose Mexican subsidiary manufactures an indoor-outdoor thermometer, has estimated that the total weekly revenue (in dollars) for producing x thermometers is R(x) = -0.04x² + 800x Similarly, they determined their total weekly cost (in dollars) for producing x thermometers is C(x) = 130x – 40,000. %3D a) Find the profit function P(x). b) Find the marginal profit function P'(x), which is the derivative of P(x). c) What is the largest possible profit that the restaurant could make in one month?

Q: A total-cost function is given by C(x) = 1700(x² +5)¹/³ +800 where C'(x) is the total cost, in…

A: the given cost function C(x)=1700(x2+5)(1/3)+800 , for the production of x airplanesrate of change…

Q: The function y = 2x2 - ln 4x (x 7 0) has one minimum point. Find its first coordinate.

A: Given  y = 2x2 - ln 4x

Q: In other words, evaluate: V(5) = 25000(0.75), rounding the proper decimal place for money.

A:

Q: Given f(x) = + 5, find the domain and range of f-'(x). %3D X – 3

A:

Q: Find f. f"(x) = 6 + 6x + 24x2, f(0) = 2, f(1) = 12 f(x) =

A:

Q: Pure Water Enterprises finds that the marginal profit, in dollars, from drilling a well that is x…

A: The marginal profit is defined as the first order derivative of the profit function. So, we can…

Q: If f(x) = x2/(4 + x), find f "(2). f "(2) =

A: f(x) = x2 /(4+x)  f'(x) = [(4+x)(2x) - x2(1)] / (4+x)2  = (8x+2x2 - x2)/(4+x)2 = (8x+x2)/(4+x)2…

Q: Find the slope of the graph of the function x2+y2=xy+1/4 at (1/2 , 1/2)

A: Given function is Differentiating both sides with respect to x, we get

Q: If f(x) = x²/(1 + x), find f "(1). f"(1) = %3D %3D

A:

Q: If g(x) = f(x) + h(x); find g'(x).

A: Topic = Derivative

Q: If f(x) = 16, find f'(7).

A: Please refer the attached image for complete solution.

Q: Differentiate the function. h(x) 4 xS - 4x3 + 1)8 5, x5 – 4x³ + h'(x) = %3!

A: We will use chain rule to solve this problem;

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.