sections 1.3 - 1.4\nscore: 2/21 answered: 2/21\nquestion 3\nfind the average rate of change of ( g(x)=-3…
sections 1.3 - 1.4\nscore: 2/21 answered: 2/21\nquestion 3\nfind the average rate of change of ( g(x)=-3 x^{3}-1 ) from ( x=-4 ) to ( x = 1 )
Answer
Explanation:
Step1: Recall the formula for average rate of change
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 = 1), and (g(x)=-3x^{3}-1).
Step2: Calculate (g(a)) and (g(b))
- For (x=a=-4): (g(-4)=-3(-4)^{3}-1=-3\times(-64)-1 = 192 - 1=191)
- For (x = b = 1): (g(1)=-3(1)^{3}-1=-3 - 1=-4)
Step3: Substitute into the average - rate - of - change formula
(\frac{g(1)-g(-4)}{1-(-4)}=\frac{-4 - 191}{1 + 4}=\frac{-195}{5}=-39)
Answer:
(-39)