Chapter 2: Q. 67 (page 91)

$f (x) = x^{2} - 2$
(a) Find the average rate of change from $- 2$ to $1 .$
(b) Find the equation of the secant line containing $(- 2, g (- 2))$ and $(1, g (1))$ .

Short Answer

Expert verified

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

(b) The equation of the secant line is $y = - x - 4$ .

Step by step solution

Step 1. Given information.

We have:

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

Part a. Step 1. Find the average rate of change from -2 to 1.

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

Average rate of change is given by:

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

Here, $a = - 2, b = 1$ :

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

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

The function is $f (x) = x^{2} - 2$ and the points $(- 2, f (- 2))$ and $(1, f (1))$ .

Substitute $x = - 2$ :

$f (- 2) = {(- 2)}^{2} - 2 = 4 - 2 = 2$

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

role="math" localid="1646231097885" $m = - 1$

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

$y - y_{1} = m_{\sec} (x - x_{1}) y - 2 = - 1 (x - (- 2)) y + 2 = - 1 (x + 2) y = - x - 2 - 2 y = - x - 4$

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$f (x) = x^{2} - 2$
(a) Find the average rate of change from $- 2$ to $1 .$
(b) Find the equation of the secant line containing $(- 2, g (- 2))$ and $(1, g (1))$ .

Short Answer

Step by step solution

Step 1. Given information.

Part a. Step 1. Find the average rate of change from -2 to 1.

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

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f(x)=x2-2(a) Find the average rate of change from -2to 1.(b) Find the equation of the secant line containing-2,g-2and1,g1.

Short Answer

Step by step solution

Step 1. Given information.

Part a. Step 1. Find the average rate of change from -2 to 1.

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

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Mechanics Maths

Probability and Statistics

Calculus

Applied Mathematics

Theoretical and Mathematical Physics

Decision Maths

Study anywhere. Anytime. Across all devices.

$f (x) = x^{2} - 2$
(a) Find the average rate of change from $- 2$ to $1 .$
(b) Find the equation of the secant line containing $(- 2, g (- 2))$ and $(1, g (1))$ .