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

• A. $3$
• B. $1$
• C. $0$
• D. $2$

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]. It is given by: (f(b) - f(a)) / (b - a).
2. Step 2: Identify the interval [a, b] from the problem. Here, a = -1 and b = 2.
3. Step 3: Substitute the values of a and b into the function f(x) = x^2 to find f(a) and f(b). Calculate f(-1) = (-1)^2 and f(2) = (2)^2.
4. Step 4: Plug the values of f(-1) and f(2) into the formula for the average rate of change: (f(2) - f(-1)) / (2 - (-1)).
5. Step 5: Simplify the numerator and denominator to compute the average rate of change. Ensure proper handling of subtraction and division.