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Chapter 4: Q. 9 (page 241)

Solve the inequality by using the graph of the function.

Solvef(x)<0, wheref(x)=x2(x-3)

Short Answer

Expert verified

The solution of the inequality is(-鈭�,0)鈭�(0,3).

Step by step solution

01

Step 1. Graph the function

The graph of the function f(x)=x2(x-3)is given as

02

Step 2. Solve the inequality

To find the solution of f(x)<0, we need to find the values of x for which the graph is below the x axis.

From the graph, we can see that for x<3 the graph is below the x axis. But at x=0, the function value is equal to0.

So the solution is given as (-鈭�,0)鈭�(0,3).

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Most popular questions from this chapter

In physics, it is established that the acceleration

due to gravity, g (in meters/sec2), at a height h meters above

sea level is given by

g(h)=3.99脳1014(6.374脳106+h)2

where6.374脳106is the radius of Earth in meters.

(a) What is the acceleration due to gravity at sea level?

(b)

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What is the acceleration due to gravity at the top of the

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(c) The peak of Mount Everest is 8848 meters above sea

level. What is the acceleration due to gravity on the

peak of Mount Everest?

(d) Find the horizontal asymptote of g(h).

(e) Solve g(h)=0. How do you interpret your answer?

Find the vertical, horizontal, and oblique asymptotes, if any, of each rational function.

G(x)=x4-1x2-x

Graph each rational function using transformations.

F(x)=2-1x+1

Graph each rational function using transformations.

R(x)=x-4x

A can in the shape of a right circular cylinder is required to have a volume of 500cubic centimeters. The top and bottom are made of material that costs 0.06鈧�per square centimeter, while the sides are made of material that costs 0.04鈧�per square centimeter.

Part (a) Express the total cost C of the material as a function of the radius r of the cylinder.

Part (b): Graph C=Cr. For what value of r is the cost C a minimum?

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