13. $f(x)=4x^{3}-20$ what is the average rate of change of $f(x)$ on the interval $1,3$? a. 2 b. 52 c. 36 d…
13. $f(x)=4x^{3}-20$ what is the average rate of change of $f(x)$ on the interval $1,3$? a. 2 b. 52 c. 36 d. 72 e. 104
Answer
Explanation:
Step1: Recall the formula for average rate of change
The average rate of change of a function (y = f(x)) on the interval ([a,b]) is (\frac{f(b)-f(a)}{b - a}). Here (a = 1), (b=3), and (f(x)=4x^{3}-20).
Step2: Calculate (f(1)) and (f(3))
- For (x = 1): (f(1)=4\times(1)^{3}-20=4 - 20=- 16)
- For (x = 3): (f(3)=4\times(3)^{3}-20=4\times27-20=108 - 20 = 88)
Step3: Substitute into the average - rate - of - change formula
(\frac{f(3)-f(1)}{3 - 1}=\frac{88-(-16)}{2}=\frac{88 + 16}{2}=\frac{104}{2}=52)
Answer:
B. 52