Problem 57 - College Algebra

Question

Find the average rate of change of the function from \(x_{1}\) to \(x_{2}.\) $$f(x)=x^{2}+2 x \text { from } x_{1}=3 \text { to } x_{2}=5$$

Step-by-Step Solution

Answer

The average rate of change of the function from \(x_1=3\) to \(x_2=5\) is \(10.\)

Step 1: Define the function

The given function in the problem is \(f(x) = x^2 + 2x\).

Step 2: Calculate the values of function at \(x_1\) and \(x_2\)

Substitute \(x_1=3\) into the function to get \(f(3)=(3)^2+2*(3)=9+6=15\). Substitute \(x_2=5\) into the function to get \(f(5)=(5)^2+2*(5)=25+10=35\).

Step 3: Apply the average rate of change formula

The average rate of change is given by the formula: \(\frac{f(x_2)-f(x_1)}{x_2-x_1}\). Substituting the given points and the values obtained in step 2 into this formula gives \((35-15)/(5-3)=20/2=10\).