f(x)=x^{2}+10\nwhat is the average rate of change of f over the interval -2,-1?
f(x)=x^{2}+10\nwhat is the average rate of change of f over the interval -2,-1?
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 = - 1).
Step2: Calculate (f(-2)) and (f(-1))
For (x=-2), (f(-2)=(-2)^{2}+10=4 + 10=14). For (x=-1), (f(-1)=(-1)^{2}+10=1 + 10=11).
Step3: Substitute into the formula
(\frac{f(-1)-f(-2)}{-1-(-2)}=\frac{11 - 14}{-1 + 2}=\frac{-3}{1}=-3)
Answer:
(-3)