Chapter 2: Q. 64 (page 91)

Find the average rate of change of $h (x) = x^{2} - 2 x + 3$
(a) From $- 1$ to $1$
(b) From $0$ to $2$
(c) From $2$ to $5$

Short Answer

Expert verified

(a) The average rate of change is $- 1 .$

(b) The average rate of change is $0 .$

Step by step solution

Step 1. Given information.

We have:

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

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

The function is $h (x) = x^{2} - 2 x + 3$ .

Average rate of change is given by:

localid="1646220271324" $\frac{∆ y}{∆ x} = \frac{f (b) - f (a)}{b - a}$

Here, $a = - 1, b = 1$ :

localid="1646220297606" $\frac{∆ y}{∆ x} = \frac{f (1) - f (- 1)}{1 - (- 1)} = \frac{{(1)}^{2} - 2 (1) + 1 - ({(- 1)}^{2} - 2 (- 1) + 1)}{1 + 1} = - 2$

Part b. Step 1. Find the average rate of change from 0 to 2.

The function is $h (x) = x^{2} - 2 x + 3$ .

Average rate of change is given by:

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

Here, $a = 0, b = 2$ :

role="math" localid="1646220402827" $\frac{∆ y}{∆ x} = \frac{f (2) - f (0)}{2 - 0} = \frac{{(2)}^{2} - 2 (2) + 1 - ({(0)}^{2} - 2 (0) + 1)}{2} = 0$

Part c. Step 1. Find the average rate of change from 2 to 5.

The function is $h (x) = x^{2} - 2 x + 3$ .

Average rate of change is given by:

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

Here, $a = 2, b = 5$ :

$\frac{∆ y}{∆ x} = \frac{f (5) - f (2)}{5 - 2} = \frac{{(5)}^{2} - 2 (5) + 1 - ({(2)}^{2} - 2 (2) + 1)}{3} = 5$

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Find the average rate of change of $h (x) = x^{2} - 2 x + 3$
(a) From $- 1$ to $1$
(b) From $0$ to $2$
(c) From $2$ to $5$

Short Answer

Step by step solution

Step 1. Given information.

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

Part b. Step 1. Find the average rate of change from 0 to 2.

Part c. Step 1. Find the average rate of change from 2 to 5.

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Find the average rate of change of hx=x2-2x+3(a) From-1to1(b) From 0to 2(c) From2to5

Short Answer

Step by step solution

Step 1. Given information.

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

Part b. Step 1. Find the average rate of change from 0 to 2.

Part c. Step 1. Find the average rate of change from 2 to 5.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Discrete Mathematics

Calculus

Mechanics Maths

Pure Maths

Theoretical and Mathematical Physics

Geometry

Study anywhere. Anytime. Across all devices.

Find the average rate of change of $h (x) = x^{2} - 2 x + 3$
(a) From $- 1$ to $1$
(b) From $0$ to $2$
(c) From $2$ to $5$