find the average rate of change of ( g(x)=-3 x^{3}-2 ) from ( x=-4 ) to ( x = 3 )
find the average rate of change of ( g(x)=-3 x^{3}-2 ) from ( x=-4 ) to ( x = 3 )
Answer
Explanation:
Step1: Recall the formula for average rate of change
The formula for the average rate of change of a function (y = g(x)) from (x=a) to (x = b) is (\frac{g(b)-g(a)}{b - a}). Here, (a=-4), (b = 3), and (g(x)=-3x^{3}-2).
Step2: Calculate (g(a)) and (g(b))
- Calculate (g(-4)): Substitute (x=-4) into (g(x)): (g(-4)=-3(-4)^{3}-2=-3(-64)-2 = 192-2=190).
- Calculate (g(3)): Substitute (x = 3) into (g(x)): (g(3)=-3(3)^{3}-2=-3\times27-2=-81 - 2=-83).
Step3: Substitute into the average - rate - of - change formula
(\frac{g(3)-g(-4)}{3-(-4)}=\frac{-83 - 190}{3 + 4}=\frac{-273}{7}=-39).
Answer:
(-39)