For the function $f\left(x\right)=2x^2+3x$, what is the average rate of change from $x=0$ to $x=5$?

• A. $28$
• B. $23$
• C. $13$
• D. $17$

Answer: (B)

Verified step by step guidance

1. Step 1: Recall the formula for the average rate of change of a function f(x) over an interval [a, b]. It is given by: \( \text{Average Rate of Change} = \frac{f(b) - f(a)}{b - a} \).
2. Step 2: Identify the interval [a, b] from the problem. Here, \( a = 0 \) and \( b = 5 \).
3. Step 3: Substitute \( a = 0 \) and \( b = 5 \) into the formula. This gives: \( \text{Average Rate of Change} = \frac{f(5) - f(0)}{5 - 0} \).
4. Step 4: Compute \( f(5) \) and \( f(0) \) using the given function \( f(x) = 2x^2 + 3x \). For \( f(5) \), substitute \( x = 5 \) into the function: \( f(5) = 2(5)^2 + 3(5) \). For \( f(0) \), substitute \( x = 0 \) into the function: \( f(0) = 2(0)^2 + 3(0) \).
5. Step 5: Plug the values of \( f(5) \) and \( f(0) \) back into the formula \( \text{Average Rate of Change} = \frac{f(5) - f(0)}{5 - 0} \) and simplify the expression to find the average rate of change.