Question

Compare the average rates of change for ​f(x)equals=3 x plus 23x+2​, ​g(x)equals=3 x squared plus 23x2+2​, and ​h(x)equals=3 Superscript x3x over the interval xequals=33 to xequals=66. Which function has the greatest average rate of​ change?
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Part 1
The average rates of change over xequals=33 to xequals=66 are enter your response here​, and
▼
g(x)
f(x)
h(x)
has the greatest average rate of change over this interval.

Answer 1

Assuming the functions are f(x)=3x+2, g(x)=3x^2+2, h(x)=3^x and the interval is x = 3 to x = 6:

- f: (f(6)-f(3))/(6-3) = ( (3·6+2) - (3·3+2) )/3 = (20-11)/3 = 9/3 = 3
- g: (g(6)-g(3))/(6-3) = ( (3·6^2+2) - (3·3^2+2) )/3 = (110-29)/3 = 81/3 = 27
- h: (h(6)-h(3))/(6-3) = (3^6 - 3^3)/3 = (729-27)/3 = 702/3 = 234

Thus the average rates of change are f = 3, g = 27, h = 234, and h(x)=3^x has the greatest average rate of change.