8x^2
from 1 to A
AROC = (f(b)-f(a))/b-a
so start plug them in
(f(a)-f(1))/a-1
plug in a
=8a^2
plug in 1
=8
so (8a^2-(8))/a-1=96
multiply both side by (a-1)
so 8a^2-8=96(a-1
distribute the right side 96(a-1)
=96a-96
so now you have
so 8a^2-8=96a-96
add 8 to both sides
so 8a^2=96a-88
factor an 8 out on both sides
so 8(a^2)=8(12a-11)
divide both sides by 8
so a^2=12a-11
put everything on one side
a^2-12a+11
now just factor or use pythagorean theorem but the factors are -11 and -1
so (a-1)(a-11)
set them equal to zero
so a=1 or a=11
now that the question is asking for a rate of change from 1 to A and it equals 96 you know that from 1 to 1 can not equal 96. they would just cancel. So the answer is 11.
A=11