(b) Consider the function f(x) = x(r+2)(6 – x). %3D i) Sketch the graph y = f(x), showing all essential features. ii) Hence solve the inequality f() > 0 for r. iii) Show that f(r) = g(x) – 4, where g(r) = -r³ + 4x² + 12x + 4. iv) Hence solve g(x) < 4 for x.

(b) Consider the function f(x) = x(r+2)(6 – x). %3D i) Sketch the graph y = f(x), showing all essential features. ii) Hence solve the inequality f() > 0 for r. iii) Show that f(r) = g(x) – 4, where g(r) = -r³ + 4x² + 12x + 4. iv) Hence solve g(x) < 4 for x.

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter9: Systems Of Equations And Inequalities

Section9.3: Systems Of Inequalities

Problem 19E

See similar textbooks

Related questions

Q: 1. The monthly revenue R earned by selling x lamps is R(x)= 120x-0.46x The monthly cost of producing…

A: (a) The given revenue and cost functions are,

Q: 8. For the quadratic function f(x)=2x² – 24.x+90 (a) Complete the square to put the equation into…

A: Given query is to find the the vertex form and the minimum value of f.

Q: Aki's Bicycle Designs has determined that when x hundred bicycles are built, the average cost per…

Q: Given the profit function P(x) = 1.3x – 0.01x² – 30, find the value of x at the function's optimum…

Q: Suppose a baby food complany has determined that its total revenue R for its food is given by…

A: Total revenue R for baby food is R=-x3+63x2+1200x where R is measured in dollars and x is the number…

Q: for the function f(x)=x2+2x-3 solve f(x) is less than or equal to 0 to find the solution

Q: The total profit P(x) (in thousands of dollars) from a sale of x thousand units of a new product is…

Q: Find the general and particular solution of the y"=3e³x if f(2)= k and f'(2)=k²

A: y"=3e³x if f(2)= k and f'(2)=k²

Q: Given the functions f(x) = g(x) = 2 x – 2' x - 2 determine (f • g)(x). Show your solutions in the…

A: The functions arefx=xx-2, gx=1x-2

Q: I have the cost function as C(x)=14x+500ln(x+1)+3000 and I'mtrying to figure out the total cost when…

Q: A fast-food restaurant has a cost of production C(x)=12x+140 and a revenue function R(x)=5x. When…

A: To find the time when company starts to earn profit. Company will earn profit when revenue is more…

Q: Let p= 23 - square root x and C(x)= 254 +3x, where x is the number of garden hoses that can be…

Q: solve for the function, x^3- 0.03x^2+2.4x10^-6=0, assuming stopping criterion of es=0.1

Q: where y1 = e* is one of the functions in the fundamental solution set. - %3D xy" + (2-2x)y' +(x- 2)y…

Q: Use the convolution theorem to solve 1 (s²+4)

Q: 8. Given f(x) = 2x- 5 & g(x) = 3x +4, solve for g o f(x). a. 11 - 6x b. 6x2 - 7x - 20 C. 6x - 11 d.…

Q: The total profit P(x) (in thousands of dollars) from the sale of x hundred thousand pillows is…

A: Given the profit function is : P(x)=-x3+12x2+144x-200. For maximum profit P'(x)=0. Because it will…

Q: Use separation of variables to find a solution to: k>0

Q: The revenue function is given by R(x) = 38x - 0.01x2. If production is limited to 1500 units. Find…

A: Given revenue function is, Rx=38x-0.01x2 And as production limit is 1500 unit so x≤1500

Q: Thando furniture manufacturer, determines that in order to sell x chairs, the price per chair in…

Q: What is the absolute maximum value of the function f(x) = x – 3x2 on the interval [-2, 3] ? a. None…

A: Given the function is f(x) = x3-3x2 on the interval -2, 3.

Q: The profit from the sale of x units of radiators for automobiles and y units of radiators for…

Q: 3 The profit P (in dollars) for a company that produces antivirus and system utilities software is…

Q: 2.a. Find the maximum and minimum values of the function: y = 3x² 18x +31 -

A: We have to find the maximum and minimum values of the given function y=3x2-18x+31 .

Q: 27)Use the graph to solve: a)/(x) = 0 b) (x)20 4+y=f(x) 彬

A: a) It is known that, y = 0 at x-axis.From the graph, it is observed that the x-intercepts of the…

Q: Aki's Bicycle Designs has determined that when x hundred bicycles are built, the average cost per…

A: Compare the given cost function with the general quadratic function as follows.

Q: The profit from the sale of x units of radiators for automobiles and y units of radiators for…

A: To find the value of x and y that leads to maximum profit, use lagrange multipliers function:…

Q: 1. Solve the difference x²-2x-8 <0. 2. Calculate the minimum distance from the origo to the line y =…

A: Introduction: When the product of two real quantities is positive, either both of them are positive…

Q: Q2) Find The root of the Equation fca)- x².x -3 -0 On L1, 2] using (the fixed point method), Where…

A: NOTE : There are no roots possible in the interval [1,2] of the equation f(x) = x2-x-3 = 0. The only…

Q: The Cost function C(x) and the Revenue function R(x) of a firm are given by C(x) = 4x +1200 and R(x)…

A: Given that the cost function Cx=4x+1200 and the revenue function is Rx=10x. We have to find the…

Q: P(x)= -x+ 12x-36x+400, x23 is an approximation to the total profit (in thousands of dollars) from…

Q: (a) To find where the graphs of the functions y = m¡x + b1 and y = m2x + b2 intersect, we solve for…

A: a) To find where the graphs of the functions intersect, we solve for x in the equation:…

Q: A fast-food restaurant has a cost of production C(x) = 12x + 126 and a revenue function R(x) = 5x.…

A: The profit function is the difference of the Revenue function and the Cost function. The company…

Q: An animal feed company must produce 200 kg of mixture consisting of ingredients x and x2.x costs 3…

A: we will first formulate the LPP using the given statements and then we will find the optimal…

Q: The weekly revenue for a product is given by R(x) = 132x-0.0135x, and the weekly cost is C(x) =…

Q: The revenue function R in terms of the number of units sold, a, is given as R= 280x – 0.4x? where R…

Q: The daily revenue R achieved by selling x boxes of candy is figured to be R(x) = 9.5x - 0.04x2 . The…

A: Given the daily revenue R(x)=9.5x-0.04x2And the daily cost C(x)=1.25x+250

Q: box

A: We will find out the height.

Q: 13) Given f(x) = 7x² – 4x – 2, without graphing, determine whether it has a maximum value or minimum…

Q: I want solve it in а раper 3- Show that the function y = x³ + 3x + 3 satisfy the y= + xy - 2y = 0

Q: Solve the simultaneous equations y = 1 + 3x - x2 and y = 3 – x graphically. Plot your graphs for…

Q: b- Find the solution of f(x) e-x, let x, 0 and E- 10-5

Q: As dry air moves upward, it expands and, in so doing, cools at a rate of about 1°C for each…

A: Answer for the question will Start by writing the expression describing the value of temperature…

Q: The total profit P(x) (in thousands of dollars) from the sale of x hundred thousand pillows is…

Q: Find the values of k for which the graphs of y=2k – kx and the quadratic y = x - x-1 intersect at i.…

A: “Since you have asked multiple questions in a single request, we will be answering only the 1st…

Q: 3. Find the absolute maximum value of f(x) = x³ – 3x² on the interval -15x<3 (A)–4 (B) 0 (C) 1 (D) 2…

Q: The function f(x) =px²-qx+ 32, p 0 has a minimum value of 0 when x= 4. Find the value of p and of q.…

A: The given function is f(x)=px2-qx+32. To use the minima information of the function, let us…

Q: x2 + kx + 8 is equal to the maximum Find k so that the minimum value of f (x) value of g(x) =1+4x –…

Question

Please answer only part iv .

(b) Consider the function f(x) = x(x+2)(6 – x).
i) Sketch the graph y = f(x), showing all essential features.
ii) Hence solve the inequality f(r) 2 0 for r.
iii) Show that f(r) = g(x) – 4, where g(x) = -r³ + 4.x² + 12x + 4.
iv) Hence solve g(x) < 4 for r.

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

This is a popular solution!

SEE SOLUTION Check out a sample Q&A here

Step 1

VIEW

Step 2

VIEW

Trending now

This is a popular solution!

Step by step

Solved in 2 steps with 2 images

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

$Area of a Circle$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, advanced-math and related others by exploring similar questions and additional content below.

Similar questions

To put the quadratic function f(x)=ax2+bx+c in standard form, we complete the ________________.
The total daily profit (in thousands of pesos) of a certain food company for the sale of x boxes of buko pie is given by the profit function P(x)=-0.001x^3+0.1x^2+3x-300 , where x is greater than or equal to 0 but less than or equal to 30. Determine the number of boxes of buko pie to be produced in order for the company to realize a maximum profit.
The total-revenue and total-cost funtions for producing x clocks are R(x)=500x-0.01x2 and C(x)=160x+100,000, where x is greater than equal zero and less than equal 25,000. What is the maximum annual profit?
suppose a baby food company has determined that its total revenue R for its food is given by R= -x^3 +42x^2 +735x where R is measured in dollars and x is the number of units (in thousands) produced. What production level will yield a maximum revenue? a production level of ____ thousand units will maximize revenue.
Find the point on the graphf(x)=4-x^2 that is closest to the point (0,1)