Answer :
Answer:
D.=k(x) = 2x^2
Step-by-step explanation:
Average rate of change:
Given a function y, the average rate of change S of [tex]y=f(x)[/tex] in an interval [tex](x_{s}, x_{f})[/tex] will be given by the following equation:
[tex]S = \frac{f(x_{f}) - f(x_{s})}{x_{f} - x_{s}}[/tex]
In this problem, we have that:
Interval (1,5), so [tex]x_{f} = 5, x_{s} = 1[/tex]
Then
[tex]S = \frac{f(5) - f(1)}{4}[/tex]
All options are compared to g(x).
[tex]g(x) = 1.8x^{2}[/tex]
g(5) = 1.8*(5)^2 = 45
g(1) = 1.8*(1)^2 = 1.8
[tex]S = \frac{45 - 1.8}{4} = 10.8[/tex]
Which one has a greater average rate of change?
Whichever has an average rate of change greater than 10.8.
A.=f(x) = x^2
f(5) = 5^2 = 25
f(1) = 1^2 = 1
[tex]S = \frac{25 - 1}{4} = 6.25[/tex]
Smaller than 10.8, so this is not the answer.
B.=g(x) = 1.2x^2
g(5) = 1.2*(5)^2 = 30
g(1) = 1.2*(1)^2 = 1.2
[tex]S = \frac{30 - 1.2}{4} = 7.2[/tex]
Smaller than 10.8, so this is not the answer.
C.=h(x) = 1.5x^2
h(5) = 1.5*(5)^2 = 37.5
h(1) = 1.5*(1)^2 = 1.5
[tex]S = \frac{37.5 - 1.5}{4} = 9[/tex]
Smaller than 10.8, so this is not the answer.
D.=k(x) = 2x^2
k(5) = 2*(5)^2 = 50
k(1) = 2*(1)^2 = 2
[tex]S = \frac{50 - 2}{4} = 12[/tex]
Greater than 10.8, this is the answer.