SOLUTION: What is the average rate of change of f(x)=x^3-3x+2 from -8 to -6, -2 to 2, 2 to 8

Algebra ->  Finance -> SOLUTION: What is the average rate of change of f(x)=x^3-3x+2 from -8 to -6, -2 to 2, 2 to 8      Log On


   

Question 1129226: What is the average rate of change of f(x)=x^3-3x+2 from -8 to -6, -2 to 2, 2 to 8
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

What is the average rate of change of f%28x%29=x%5E3-3x%2B2 from+-8 to -6, -2 to 2, 2+to+8
f%28-8%29=%28-8%29%5E3-3%28-8%29%2B2
f%28-8%29=-512%2B24%2B2
f%28-8%29=-486

f%28-6%29=%28-6%29%5E3-3%28-6%29%2B2
f%28-6%29=-216%2B18%2B2
f%28-6%29=-196
the average rate of change from -8 to -6 is:
Given a function f(x) plotted in the Cartesian plane as y+=+f%28x%29, the average rate of change (or average rate of change function) of f from x to a is given by

A(x,+a) = %28f%28x%29+-+f%28a%29%29%2F%28x+-+a%29=>x=-8 and a=-6
since f%28-8%29=-486 and f%28-6%29=-196, we have
A(-8,+-6) = %28-486+-+%28-196%29%29%2F%28-8+-+%28-6%29%29
A(-8,+-6) = %28-486+%2B196%29%2F%28-8+%2B6%29
A(-8,+-6) = %28-290%29%2F%28-2%29
A(-8,+-6) = 145

f%28-2%29=%28-2%29%5E3-3%28-2%29%2B2
f%28-2%29=-8%2B6%2B2
f%28-2%29=0

f%282%29=2%5E3-3%282%29%2B2
f%282%29=8-6%2B2
f%282%29=4
the average rate of change from -2 to 2 is:
A(-2,+2) = %280+-+4%29%2F%28-2+-+2%29
A(-2,+2) = %28+-+4%29%2F%28-4%29
A(-2,+2) = 1


f%282%29=2%5E3-3%282%29%2B2
f%282%29=8-6%2B2
f%282%29=4

f%288%29=8%5E3-3%288%29%2B2
f%288%29=512-24%2B2
f%288%29=490


the average rate of change from 2 to 8 is:
A(2,+8) = %284+-+490%29%2F%282+-+8%29
A(2,+8) = %28+-+486%29%2F%28+-+6%29
A(2,+8) = 81