Problem

Given a function \( f(x) = 2x^2 + 3x + 1 \), find the average rate of change of \( f \) on the interval \( [1, 4] \).

Answer

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Answer

Step 4: Substitute the results from Step 1 and Step 2 into the formula above, we get \( \frac{41 - 6}{4 - 1} = \frac{35}{3} \).

Steps

Step 1 ：Step 1: Substitute \( x = 1 \) into the function, we get \( f(1) = 2(1)^2 + 3*1 + 1 = 6 \).

Step 2 ：Step 2: Substitute \( x = 4 \) into the function, we get \( f(4) = 2(4)^2 + 3*4 + 1 = 41 \).

Step 3 ：Step 3: The average rate of change of \( f \) on the interval \( [1, 4] \) is equal to \( \frac{f(4) - f(1)}{4 - 1} \).

Step 4 ：Step 4: Substitute the results from Step 1 and Step 2 into the formula above, we get \( \frac{41 - 6}{4 - 1} = \frac{35}{3} \).

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