determine the average rate of change of f(x) over the interval -2, 3.
determine the average rate of change of f(x) over the interval -2, 3.
Answer
Explanation:
Step1: Recall the formula for average rate of change
The formula for the average rate of change of a function (y = f(x)) over the interval ([a,b]) is (\frac{f(b)-f(a)}{b - a}). Here, (a=-2) and (b = 3).
Step2: Find (f(a)) and (f(b))
From the table, when (x=-2), (f(-2)=-3) (so (f(a)=f(-2)=-3)), and when (x = 3), (f(3)=12) (so (f(b)=f(3)=12)).
Step3: Substitute into the formula
Substitute (a=-2), (b = 3), (f(a)=-3), and (f(b)=12) into (\frac{f(b)-f(a)}{b - a}). We get (\frac{12-(-3)}{3-(-2)}). Simplify the numerator: (12-(-3)=12 + 3=15). Simplify the denominator: (3-(-2)=3 + 2=5). So, (\frac{15}{5}=3).
Answer:
(3)