SOLUTION: How do I find the average rate of change for G(x) = 3x^3 - 5x. From x=a, to x=t How do I find the average rate of change: F(x) = 3/(x^2) - 2x. ARC from a to b. Please help

Algebra ->  Equations -> SOLUTION: How do I find the average rate of change for G(x) = 3x^3 - 5x. From x=a, to x=t How do I find the average rate of change: F(x) = 3/(x^2) - 2x. ARC from a to b. Please help       Log On


   

Question 949897: How do I find the average rate of change for G(x) = 3x^3 - 5x. From x=a, to x=t

How do I find the average rate of change: F(x) = 3/(x^2) - 2x. ARC from a to b.
Please help
Thank you
Found 2 solutions by josgarithmetic, stanbon:
Answer by josgarithmetic(39616) About Me  (Show Source):
You can put this solution on YOUR website!
The interval for the change on the x-axis is t-a.
The G values change from 3t%5E3-5t-%283a%5E3-5a%29 or 3t%5E3-5t-3a%5E3%2B5a.
The average rate of change is %283t%5E3-5t-3a%5E3%2B5a%29%2F%28t-a%29.

Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
Average = (f(a)-f(t))/(a-t)
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find the average rate of change for G(x) = 3x^3 - 5x. From x=a, to x=t
ave = [3a^3-5a - (3t^3-5t)] / (a-t)
= [3(a^3-t^3)-5(a-t)] / [a-t]
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= [a^2+at+t^2 - 5]
============================

How do I find the average rate of change: F(x) = 3/(x^2) - 2x. ARC from a to b.
Ave = [[3/a^2)-(2a) - [(3/b^2)-2b]] / (a-b)
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= [3[1/a^2- 1/b^2]-[2(a-b)]/(a-b)
----
= [-3(a^2-b^2)/a^2b^2 - 2(a-b)]/(a-b)
------------------
= [-3(a+b)/a^2b^2 - 2]
===========================
Cheers,
Stan H.