Question

f(x)=x^{2}+10
what is the average rate of change of f over the interval -2,-1?

Explanation:

Step1: Recall the average rate of change formula

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 \(a=-2\), \(b = - 1\).

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:

\(-3\)