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Chapter 4: Q. 83 (page 243)

The inequality $x^{4} + 1 < - 5$ has no solution. Explain why.

Short Answer

Expert verified

Because $x^{4} + 1$ is always positive.

Hence, the given inequality has no solutions.

Step by step solution

01

Given information

The given inequality is $x^{4} + 1 < - 5$

02

Determine the solution of the given inequality,

$x^{4}$ always satisfies the inequality $x^{4} \geq 0$ .

Example: $- 1 \cdot - 1 \cdot - 1 \cdot - 1 = 1$

So, $x^{4} + 1 \geq 0$ .

03

Write the conclusion

$x^{4} + 1 \geq 0$ is always positive

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Most popular questions from this chapter

In Problems 63–72, find the real solutions of each equation.

$x^{4} - x^{3} + 2 x^{2} - 4 x - 8 = 0$

Use the Factor Theorem to prove that $x + c$ is a factor of

role="math" localid="1646067091231" $x^{n} + c^{n}$ if $n \geq 1$ is an odd integer

One solution of the equation $x^{3} - 8 x^{2} + 16 x - 3 = 0$ is $3$ .

Find the sum of the remaining solutions.

True or False The graph of a rational function may intersect a vertical asymptote.

United Parcel Service has contracted you to design a closed box with a square base that has a volume of $10, 000$ cubic inches. See the illustration.

Part (a): Express the surface area S of the box as a function of x.

Part (b): Using a graphing utility, graph the function found in part (a).

Part (c): What is the minimum amount of cardboard that can be used to construct the box?

Part (d): What are the dimensions of the box that minimize the surface are?

Part (e): Why might UPS be interested in designing a box that minimizes the surface area?

See all solutions

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