Concept explainers
(a)
The graph of the function
(a)

Answer to Problem 72E
The graph is obtained along the negative axis.
Explanation of Solution
Given information:
The polynomial function is shown below,
Formula used:
The horizontal axis is x axis and the vertical axis is y axis.
Calculation:
The leading coefficient test says that: 1. If the degree of the polynomial is even and the leading coefficient is positive, both ends of the graph rise up 2. If the degree is even and the leading coefficient is negative, both ends of the graph fall down 3. If the degree is odd and the leading coefficient is positive, the left side of the graph falls down and the right side rises up 4. If the degree is odd and the leading coefficient is negative, the left side of the graph rises up and the right side falls down.
As the leading coefficient is negative and degree is even, both ends of the graph fall down. The ends of the graph would be in the direction as shown below:
Conclusion:
The graph is obtained along the negative axis.
(b)
The zeros of the polynomial.
(b)

Answer to Problem 72E
The zeros of the polynomial is 2, 8.
Explanation of Solution
Given information:
The polynomial function is shown below,
Formula used:
The polynomial is equated to zero.
Calculation:
Putting
Adding these points to the graph, and get
Conclusion:
The zeros of the polynomial is 2, 8.
(c)
The plotting sufficient solution points.
(c)

Answer to Problem 72E
The value gets increases and decreases continuously.
Explanation of Solution
Given information:
The polynomial function is shown below,
Formula used:
The test interval is determined by the values of the zeros.
Calculation:
The polynomial function is evaluated at the values chosen between the test intervals. And the test interval is determined by the values of the zeros. Consider the table of values shown below,
Conclusion:
The value gets increases and decreases continuously.
(d)
The continuous curve through the points.
(d)

Answer to Problem 72E
The graph cuts the x-axis at x = 2, 8.
Explanation of Solution
Given information:
The polynomial function is shown below,
Formula used:
The values are plotted against the x- axis and y-axis.
Calculation:
A continuous curve through the points obtained in the table is drawn. It is to be noted that as both the zeros are of odd multiplicity, the graph cuts the x-axis at x = 2, 8.
Conclusion:
The graph cuts the x-axis at x = 2, 8.
Chapter 2 Solutions
EBK PRECALCULUS W/LIMITS
- A body of mass m at the top of a 100 m high tower is thrown vertically upward with an initial velocity of 10 m/s. Assume that the air resistance FD acting on the body is proportional to the velocity V, so that FD=kV. Taking g = 9.75 m/s2 and k/m = 5 s, determine: a) what height the body will reach at the top of the tower, b) how long it will take the body to touch the ground, and c) the velocity of the body when it touches the ground.arrow_forwardA chemical reaction involving the interaction of two substances A and B to form a new compound X is called a second order reaction. In such cases it is observed that the rate of reaction (or the rate at which the new compound is formed) is proportional to the product of the remaining amounts of the two original substances. If a molecule of A and a molecule of B combine to form a molecule of X (i.e., the reaction equation is A + B ⮕ X), then the differential equation describing this specific reaction can be expressed as: dx/dt = k(a-x)(b-x) where k is a positive constant, a and b are the initial concentrations of the reactants A and B, respectively, and x(t) is the concentration of the new compound at any time t. Assuming that no amount of compound X is present at the start, obtain a relationship for x(t). What happens when t ⮕∞?arrow_forwardConsider a body of mass m dropped from rest at t = 0. The body falls under the influence of gravity, and the air resistance FD opposing the motion is assumed to be proportional to the square of the velocity, so that FD = kV2. Call x the vertical distance and take the positive direction of the x-axis downward, with origin at the initial position of the body. Obtain relationships for the velocity and position of the body as a function of time t.arrow_forward
- Assuming that the rate of change of the price P of a certain commodity is proportional to the difference between demand D and supply S at any time t, the differential equations describing the price fluctuations with respect to time can be expressed as: dP/dt = k(D - s) where k is the proportionality constant whose value depends on the specific commodity. Solve the above differential equation by expressing supply and demand as simply linear functions of price in the form S = aP - b and D = e - fParrow_forwardFind the area of the surface obtained by rotating the circle x² + y² = r² about the line y = r.arrow_forward1) Find the equation of the tangent line to the graph y=xe at the point (1, 1).arrow_forward
- 3) Suppose that f is differentiable on [0, 5], and f'(x) ≤ 3 over this interval. If f(0) = −1, what is the maximum possible value of f(5)?arrow_forward2) Find the maximum value of f(x, y) = x - y on the circle x² + y² - 4x - 2y - 4 = 0.arrow_forwardFor the system consisting of the lines: and 71 = (-8,5,6) + t(4, −5,3) 72 = (0, −24,9) + u(−1, 6, −3) a) State whether the two lines are parallel or not and justify your answer. b) Find the point of intersection, if possible, and classify the system based on the number of points of intersection and how the lines are related. Show a complete solution process.arrow_forward
- 3. [-/2 Points] DETAILS MY NOTES SESSCALCET2 7.4.013. Find the exact length of the curve. y = In(sec x), 0 ≤ x ≤ π/4arrow_forwardH.w WI M Wz A Sindax Sind dy max Утах at 0.75m from A w=6KN/M L=2 W2=9 KN/m P= 10 KN B Make the solution handwritten and not artificial intelligence because I will give a bad rating if you solve it with artificial intelligencearrow_forwardSolve by DrWz WI P L B dy Sind Ⓡ de max ⑦Ymax dx Solve by Dr ③Yat 0.75m from A w=6KN/M L=2 W2=9 kN/m P= 10 KN Solve By Drarrow_forward
- Calculus: Early TranscendentalsCalculusISBN:9781285741550Author:James StewartPublisher:Cengage LearningThomas' Calculus (14th Edition)CalculusISBN:9780134438986Author:Joel R. Hass, Christopher E. Heil, Maurice D. WeirPublisher:PEARSONCalculus: Early Transcendentals (3rd Edition)CalculusISBN:9780134763644Author:William L. Briggs, Lyle Cochran, Bernard Gillett, Eric SchulzPublisher:PEARSON
- Calculus: Early TranscendentalsCalculusISBN:9781319050740Author:Jon Rogawski, Colin Adams, Robert FranzosaPublisher:W. H. FreemanCalculus: Early Transcendental FunctionsCalculusISBN:9781337552516Author:Ron Larson, Bruce H. EdwardsPublisher:Cengage Learning





