Question

find the average rate of change of ( f(x)=-4x + 3 ) from 3 to 6.
the average rate of change of ( f(x)=-4x + 3 ) from 3 to 6 is (square).
(simplify your answer.)

Explanation:

Step1: Recall the formula for average rate of change

The formula for the average rate of change of a function \(y = f(x)\) from \(x=a\) to \(x = b\) is \(\frac{f(b)-f(a)}{b - a}\). Here, \(a = 3\), \(b=6\), and \(f(x)=-4x + 3\).

Step2: Calculate \(f(3)\) and \(f(6)\)

• For \(x = 3\): \(f(3)=-4\times3+3=-12 + 3=-9\).
• For \(x = 6\): \(f(6)=-4\times6+3=-24 + 3=-21\).

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

\(\frac{f(6)-f(3)}{6 - 3}=\frac{-21-(-9)}{6 - 3}=\frac{-21 + 9}{3}\).

Step4: Simplify the expression

\(\frac{-12}{3}=-4\).

Answer:

\(-4\)