Answer:
44
Step-by-step explanation:
Given:
[tex] f(x) = 4x^2 - 3 [/tex]
Required:
Average range of change from 3 to 9
SOLUTION:
Step 1:
Find f(3) and f(9):
To find f(3), replace x with 3 in the given function
[tex] f(3) = 4(3)^2 - 3 [/tex]
[tex] f(3) = 4(9) - 3 [/tex]
[tex] f(3) = 36 - 3 [/tex]
[tex] f(3) = 33 [/tex]
To find f(9), replace x with 9 in the given function
[tex] f(9) = 4(9)^2 - 3 [/tex]
[tex] f(9) = 4(81) - 3 [/tex]
[tex] f(9) = 324 - 3 [/tex]
[tex] f(9) = 321 [/tex]
Average rate of change = [tex] \frac{f(b) - f(a)}{b - a} [/tex]
Where,
[tex] a = 3, f(a) = 33 [/tex]
[tex] b = 9, f(b) = 321 [/tex]
Plug in the values into the formula for average rate of change.
[tex] = \frac{321 - 33}{9 - 3} [/tex]
[tex] = \frac{288}{6} [/tex]
[tex] = 44 [/tex]
Average rate of change = 44
