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Precalculus Enhanced with Graphing Utilities

Sullivan

$Math Studyset 91影视 Explanations$ Math

6th Edition 路 1200 pages

ISBN: 9780321795465

Chapter 2: Q. 70 (page 91)

$h (x) = - 2 x^{2} + x$
(a) Find the average rate of change from $0$ to $3 .$
(b) Find the equation of the secant line containing $(0, h (0))$ and $(3, h (3))$ .

Short Answer

Expert verified

(a) The average rate of change is $- 5 .$

(b) The equation of the secant line is $y = - 5 x .$

Step by step solution

01

Step 1. Given information.

We have:

$h (x) = - 2 x^{2} + x$

02

Part a. Step 1. Find the average rate of change from 0 to 3.

The function is $h (x) = - 2 x^{2} + x$ .

Average rate of change is given by:

$\frac{鈭� y}{鈭� x} = \frac{f (b) - f (a)}{b - a}$

Here, $a = 0, b = 3 :$

$\frac{鈭� y}{鈭� x} = \frac{f (3) - f (0)}{3 - 0} \frac{鈭� y}{鈭� x} = \frac{- 2 {(3)}^{2} + 3 - (- 2 {(0)}^{2} + 0)}{3} = - 5$

03

Part b. Step 1. Find the equation of the secant line.

The function is $h (x) = - 2 x^{2} + x$ and the points $(0, h (0))$ and $(3, h (2))$ .

Substitute $x = 0 :$

$h (0) = - 2 {(0)}^{2} + 0 h (0) = 0$

The slope of the secant line is equal to the average rate of change of a function, it follows:

$m = - 5$

Therefore, use the point-slope form to equation of the secant line:

$y - y_{1} = m_{\sec} (x - x_{1}) y - 0 = - 5 (x - 0) y = - 5 x$

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Most popular questions from this chapter

True or False The domain of $(f . g) (x)$ consists of the numbers $x$ that are in the domains of both $f and g$ .

True or False

To obtain the graph of $f (x) = \sqrt{x + 2}$ , shift the graph of $y = \sqrt{x}$ horizontally to the right $2$ units.

In Problems 33鈥� 44, determine algebraically whether each function is even, odd, or neither.

$h (x) = \frac{- x^{3}}{3 x^{2} - 9}$

Graph the function using the techniques of shifting, compressing, stretching, and/or reflecting. Start with the graph of the basic function and show all stages. Be sure to show at least three key points. Find the domain and the range of each function. Verify your results using a graphing utility.

$f (x) = {(x + 2)}^{3} - 3$

In March $2011$ , Nicor Gas had the following rate schedule for natural gas usage in single-family residences:

Monthly customer charge $- \(13.55$

Distribution charge

First $20$ therms $- 0.1473 / t h e r m$

Next $30$ therm $- \) 0.0579 / t h e r m$

Over $50$ therm $- \(0.0519 / t h e r m$

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(a) What is the charge for using $40$ therms in a month?

(b) What is the charge for using $150$ therms in a month?

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(d) Graph the function found in part (c).

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