Given the function $f\left(x\right)=x^2$, what is the average rate of change of $f\left(x\right)$ between $x=1$ and $x=2$?

• A. $2$
• B. $1.5$
• C. $3$
• D. $4$

Answer: (A)

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]. The formula is: (f(b) - f(a)) / (b - a).
2. Step 2: Identify the interval [a, b] given in the problem. Here, a = 1 and b = 2.
3. Step 3: Substitute the values of a and b into the formula. This means calculating f(2) and f(1) using the given function f(x) = x^2.
4. Step 4: Compute f(2) by substituting x = 2 into f(x). This gives f(2) = 2^2.
5. Step 5: Compute f(1) by substituting x = 1 into f(x). This gives f(1) = 1^2. Then, substitute f(2) and f(1) into the formula for the average rate of change and simplify.