Problem 56 - College Algebra

Question

Find the average rate of change of the function from \(x_{1}\) to \(x_{2}.\) $$f(x)=6 x \text { from } x_{1}=0 \text { to } x_{2}=4$$

Step-by-Step Solution

Answer

The average rate of change of the function \(f(x) = 6x\) from \(x_{1}=0\) to \(x_{2}=4\) is 6.

Step 1: Formula for Average Rate of Change

The average rate of change of a function for an interval [a,b], can be found using the formula: \(\frac{f(b)-f(a)}{b-a}\)

Step 2: Substitution

In our problem \(f(x)\) is given by \(6x\), \(a = x_{1} = 0\), and \(b = x_{2} = 4\). This means that \(f(a) = f(0) = 6*0 = 0\), and \(f(b) = f(4) = 6*4 = 24\). Substituting these values into the formula gives us \(\frac{f(b)-f(a)}{b-a} = \frac{24 - 0}{4 - 0}\)

Step 3: Evaluate the expression

Solving the expression \(\frac{24}{4}\) , the average rate of change of the function is equal to 6.