Find the average rate of change of the function from to .
The average rate of change is . (Simplify your answer.)

Ask by Black Stewart. in the United States

Mar 25,2025

Question

Find the average rate of change of the function $$ f(x)=x^{2}+3 x $$ from $$ x_{1}=1 $$ to $$ x_{2}=2 $$. The average rate of change is $$ \square $$. (Simplify your answer.)

UpStudy AI · Accepted Answer

To find the average rate of change of the function $$ f(x) = x^{2} + 3x $$ from $$ x_{1} = 1 $$ to $$ x_{2} = 2 $$, we can use the formula for the average rate of change:

$$ \text{Average Rate of Change} = \frac{f(x_{2}) - f(x_{1})}{x_{2} - x_{1}} $$

Given:
- $$ f(x) = x^{2} + 3x $$
- $$ x_{1} = 1 $$
- $$ x_{2} = 2 $$

Let's calculate the average rate of change using the formula.
Calculate the value by following steps:
- step0: Calculate:
  $$\left(2^{2}+3\times 2\right)-\left(1^{2}+3\times 1\right)$$
- step1: Multiply the numbers:
  $$\left(2^{2}+6\right)-\left(1^{2}+3\times 1\right)$$
- step2: Add the numbers:
  $$10-\left(1^{2}+3\times 1\right)$$
- step3: Evaluate the power:
  $$10-\left(1+3\times 1\right)$$
- step4: Multiply:
  $$10-\left(1+3\right)$$
- step5: Add the numbers:
  $$10-4$$
- step6: Subtract the numbers:
  $$6$$
The average rate of change of the function $$ f(x) = x^{2} + 3x $$ from $$ x_{1} = 1 $$ to $$ x_{2} = 2 $$ is $$ \frac{6}{1} = 6 $$.
The average rate of change is 6.

Find the average rate of change of the function from to .
The average rate of change is . (Simplify your answer.)

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Find the average rate of change of the function from to . The average rate of change is . (Simplify your answer.)