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f(x) = 3x – 5. Find the average rate of change of the function between x = 3 and x = 7.

Sagot :

Given:

The function is:

[tex]f(x)=3x-5[/tex]

To find:

The average rate of change of the function between x = 3 and x = 7.

Solution:

We have,

[tex]f(x)=3x-5[/tex]

For [tex]x=3[/tex],

[tex]f(3)=3(3)-5[/tex]

[tex]f(3)=9-5[/tex]

[tex]f(3)=4[/tex]

For [tex]x=7[/tex],

[tex]f(7)=3(7)-5[/tex]

[tex]f(7)=21-5[/tex]

[tex]f(7)=16[/tex]

The average rate of change of the function f(x) between x = a and x = b is:

[tex]m=\dfrac{f(b)-f(a)}{b-a}[/tex]

The average rate of change of the function between x = 3 and x = 7 is:

[tex]m=\dfrac{f(7)-f(3)}{7-3}[/tex]

[tex]m=\dfrac{16-4}{4}[/tex]

[tex]m=\dfrac{12}{4}[/tex]

[tex]m=3[/tex]

Therefore, the average rate of change of the function between x = 3 and x = 7 is 3.

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