Chapter 4: Q94. (page 195)

Analyze each polynomial function.
$f (x) = - 1.2 x^{4} + 0.5 x^{2} - \sqrt{3} x + 2$

Short Answer

Expert verified

Consider the given function.

$f (x) = - 1.2 x^{4} + 0.5 x^{2} - \sqrt{3} x + 2$

Step by step solution

Step 1. Given information.

Consider the given function.

$f (x) = - 1.2 x^{4} + 0.5 x^{2} - \sqrt{3} x + 2$

Step 2. An Explanation for the polynomial.

The polynomial function fis of degree 4 and the graph behaves like, $y = - 1.2 x^{4}$ .

The y-intercept is (0,2) and put 0 for f(x) to find x -intercept.

$\begin{array}{rcl} - 1.2 x^{4} + 0.5 x^{2} - \sqrt{3} x + 2 & = & 0 \\ 1.2 x^{4} - 0.5 x^{2} + \sqrt{3} x - 2 & = & 0 \\ x & \approx & 0.91336, - 1.47191 \end{array}$

The given function has two turning point

Values of x on each side of the y-intercepts:

Make the table:

x	y
0	2
-1.472	0
0.913	0
-0.809	3.214

The given function has one turning point $(0.809, 3.214)$ .

The domain is the real numbers and the range is $(- \infty, 3.21445]$ .

The increasing and decreasing interval is defined as,

$Increasing : (- \infty < x < - 0.80894) Decreasing : (- 0.80894 < x < \infty)$

Step 4. The graph.

The graph of the given function is drawn as,

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Analyze each polynomial function.
$f (x) = - 1.2 x^{4} + 0.5 x^{2} - \sqrt{3} x + 2$

Short Answer

Step by step solution

Step 1. Given information.

Step 2. An Explanation for the polynomial.

Values of x on each side of the y-intercepts:

Step 4. The graph.

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Analyze each polynomial function.fx=-1.2x4+0.5x2-3x+2

Short Answer

Step by step solution

Step 1. Given information.

Step 2. An Explanation for the polynomial.

Values of x on each side of the y-intercepts:

Step 4. The graph.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Decision Maths

Geometry

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Probability and Statistics

Study anywhere. Anytime. Across all devices.

Analyze each polynomial function.
$f (x) = - 1.2 x^{4} + 0.5 x^{2} - \sqrt{3} x + 2$