f ( x ) = x ^ { 2 } - 4 x - 12

Q: A company has installed new machinery that will produce a savings rate (in thousands of dollars per…

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Q: FCX)=5 25 -x², X L5 F(X)

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Q: You are given a real number N. How should you write it as a sum of two real numbers so that their…

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Q: f (x) = 6x3 -15x2+x-4 3x2-1 ニ

A: slant asymptote of the rational function: - A slant (oblique) asymptote occurs when the numerator…

Q: Find three positive numbers whose sum is 300 and whose product is a maximum.

A: Let x ,y,z are 3 positive numbers such that x+y+z = 300 and xyz is maximumThe problem formed…

Q: Victaria Lop. 2. f(x) = x – 3x – 10 2 Зх - -

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Q: хах 1-f- '1+3x2

A: Integration is the process of finding the anti derivative of a function. There are basically two…

Q: Find two real numbers whose difference is 40 and whose product is a minimum.

A: Let the two real numbers be x & y. Since the difference is 40, therefore x-y=40⇒y=x-40   →1 Now…

Q: Find the positive integer that maximizes the sum of the numbers and its reciprocals?

A: First make equation and then differentiate

Q: Where is optimization often applied and what is its importance?

A: Solution:Optimization:Optimization methods are used in many areas of study to find solutions that…

Q: how to find break even point of the profit function p(x)=-55-6x+0.2x2

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Q: Find three positive numbers whose sum is 100 and whose product is a maximum.

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Q: 2 - 3x - f 2x-2,

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Q: Differentiate f(x) = (8x³ + 4x )(2x² +5) using product rule.

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Q: units of special lamp and the regular lamp should be produced per production period in order to…

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Q: A rectangular plot of ground is 120 m long and 80 m wide.To double the area of the plot,while…

A: For Rectangular plot,  Length = 120 m Breath = 80 m

Q: differentiate f(x)=(2x2-7)5-(1+4x3)5

A: This question is based on diffrentiation of function.

Q: Find two positive numbers whose sum equals 100 and who maximize the square root of their product. X…

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Q: Find three positive numbers whose sum is 3 and whose product is a maximum.

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Q: f(x) = 4x° - 39x - 144x+5

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Q: suppose that the selling price P of an item to the quantity x is given by  P=-1/4x +50.   0<or= x…

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Q: Use quotient Rule: 2 6. y = X-3 5. У x2 –5x + 6

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Q: 2 f(x) = (-7x4 + 10x + 8)(x2 + 10)

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Q: Solve for the maximum and minimum values for ∫(x^3−2)/3dx. (Upper limit is 1 and lower limit is -2

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Q: Sketch the graph of:

A: Given: fx=-x2-6,x≤-4x+5,x>-4 For drawing graph of given function, we will use graphing calculator

Q: Find two numbers with difference 130 and whose product is a minimum.

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Q: maximise x1 + 2x2 subject to -x1 + 2x2 < 6, x1 + 3x2 < 12, X1, X2 20

A: Linear programming, graphical method

Q: how do I solve f(x)=3x-10

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Q: An open box of maximum volume is to be made from a square piece of material, 24 inches on a side, by…

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Q: 2 The maximum value of (-3 + 4x – x + 4)2 + (x – 5)2

A: Introduction :

Q: the area of the largest rectangle that can be drawn with one side along the x-axis and the two…

A: Given curve is y=e-x2. Here the curve is symmetric about origin. Consider the vertices of rectangle…

Q: The cost per day of running a hospital is 300,000 + 0.75x2 dollars, where x is the number of…

A: Given cost equation is: C(x) = 300000 + 0.75 x^2 For x = 200 we get, C(200) = 300000 + 0.75 (200^2)…

Q: Proctice Completina th 2x716x+9=| ニ1

A: Given that: x2+6x+9=1

Q: A firm can produce only 1300 units per month. The monthly total cost is given by  C(x) = 500 + 200x…

A: Given that, the monthly total cost is, C(x)=500+200x and the total revenue is, R(x)=450x-1100x2.…

Q: The fixed costs of a business for production of a particular item over a period are $1000 while the…

A: Solution:-

Q: At a certain time of day, a tree that is x meters tall casts a shadow that is x−14x−14 meters long.…

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Q: A firm can produce only 3200 units per month. The monthly total cost is given by  C(x) = 500 + 200x…

A: Find the profit function P(x):

Q: Find two positive numbers whose sum equals 90 and who maximize the square root of their product.

A: Given that , Sum of two numbers are 90. find the numbers.

Q: Differentiate. 2) f(x) = e3x

A: As per our guidelines we are suppose to solve only first question if the multiple questions are…

Q: What is the maximum product of two numbers that add to 28? What numbers yield this product?

A: Given query is to find two numbers that add to 28 and their product will be maximum

Q: A 40-room hotel is fully occupied if $3000 is charged per day per room. For every x hundred-dollar…

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Q: Find three positive numbers whose sum is 400 and whose product is a maximum.

A: Let 3 numbers be x, y, z Sum of these numbers is 400 x+y+z = 400          z= 400-x-y Product = P(x,…

Q: The marginal profit from selling x chairs is P'(x)=-10x2 +100x+50 dollars per chair. There are no…

A: The marginal profit from selling x chairs is P'(x)=-10x2 +100x+50 dollars per chair. There are no…

Q: Differentiate f(x)=(3x-4)(5x^3-x^2+1)

A: To find the derivative we can choose two methods 1) after opening the brackets, then take…

Q: How do I express x=-10,2   in interval notation?

A:

Q: A critical communications relay has a constant failure rate of 0.1 per day. Once it has failed,…

A: Given that a critical communications relay has a constant failure rate of 0.1 per day. Once it has…

Q: Max Z = 3x1 + 182x2 %3D Subject to 9x +5x를 S 72

A: In this question, we use the KKT condition to solve the NLP. MaxZ=3x1+182x2subject…

Q: Find two numbers whose sum is 11 and product is a maximum?

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Q: suppose a baby food company has determined that its total revenue R for its food is given by R =…

A: Given:       R = - x3 + 36x2 + 540x    R is measured in dollars and X is the number of units…

Transformation of Graphs

The word ‘transformation’ means modification. Transformation of the graph of a function is a process by which we modify or change the original graph and make a new graph.

Exponential Functions

The exponential function is a type of mathematical function which is used in real-world contexts. It helps to find out the exponential decay model or exponential growth model, in mathematical models. In this topic, we will understand descriptive rules, concepts, structures, graphs, interpreter series, work formulas, and examples of functions involving exponents.