find the average rate of change of ( f(x)=-4x + 3 ) from 3 to 6.\nthe average rate of change of ( f(x)=-4x +…

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

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

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)