Chapter 2: Q. 26 (page 124)

Find the average rate of change from $2$ to $3$ for each function $f$ . Be sure to simplify.
$f (x) = 3 x - 4 x^{2}$

Short Answer

Expert verified

The average rate of change is $- 17$ .

Step by step solution

Step 1. Find f(2) and f(3)

Consider the function $f (x) = 3 x - 4 x^{2}$ .

Now the function value for $x = 2$ is given as

role="math" localid="1645897024793" $f (2) = 3 \times 2 - 4 \times 2^{2} f (2) = 6 - 4 \times 4 f (2) = 6 - 16 f (2) = - 10$

Again, the function value for $x = 3$ is given as

role="math" localid="1645897053108" $f (3) = 3 \times 3 - 4 \times 3^{2} f (3) = 9 - 4 \times 9 f (3) = 9 - 36 f (3) = - 27$

Step 2. Find the average rate of change

The average of change for the function $f (x)$ from $2$ to $3$ is given as

$\begin{array}{rcl} \frac{f (3) - f (2)}{3 - 2} & = & \frac{- 27 - (- 10)}{1} \\ = & - 27 + 10 \\ = & - 17 \end{array}$

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Find the average rate of change from $2$ to $3$ for each function $f$ . Be sure to simplify.
$f (x) = 3 x - 4 x^{2}$

Short Answer

Step by step solution

Step 1. Find f(2) and f(3)

Step 2. Find the average rate of change

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Find the average rate of change from 2to 3for each function f. Be sure to simplify. f(x)=3x-4x2

Short Answer

Step by step solution

Step 1. Find f(2) and f(3)

Step 2. Find the average rate of change

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Logic and Functions

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Study anywhere. Anytime. Across all devices.

Find the average rate of change from $2$ to $3$ for each function $f$ . Be sure to simplify.
$f (x) = 3 x - 4 x^{2}$