Question

enter the answer in the space provided. what is the average rate of change of ( f(x)=-6(2)^{x} ) from ( x = - 1 ) to ( x = 2 )?

Explanation:

Step1: Recall the average rate of change formula

The average rate of change of a function \(y = f(x)\) from \(x=a\) to \(x = b\) is \(\frac{f(b)-f(a)}{b - a}\). Here, \(a=-1\), \(b = 2\), and \(f(x)=-6(2)^{x}\).

Step2: Calculate \(f(-1)\) and \(f(2)\)

• For \(x=-1\): \(f(-1)=-6(2)^{-1}=-\frac{6}{2}=-3\).
• For \(x = 2\): \(f(2)=-6(2)^{2}=-6\times4=-24\).

Step3: Substitute into the average - rate - of - change formula

\(\frac{f(2)-f(-1)}{2-(-1)}=\frac{-24-(-3)}{2 + 1}=\frac{-24 + 3}{3}=\frac{-21}{3}=-7\).

Answer:

\(-7\)