SOLUTION: Find the average rate of change of f(x)=-x^3+3x^2 from x=-1 to x=4

Algebra ->  Functions -> SOLUTION: Find the average rate of change of f(x)=-x^3+3x^2 from x=-1 to x=4      Log On


   

Question 1127529: Find the average rate of change of f(x)=-x^3+3x^2 from x=-1 to x=4
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

f%28x%29=-x%5E3%2B3x%5E2+ from x=-1 to x=4+
average rate of change is simply the slope of the line through (-1,f%28-1%29) and (4,f%284%29)
f%28-1%29=-%28-1%29%5E3%2B3%28-1%29%5E2
f%28-1%29=1%2B3
f%28-1%29=4
f%284%29=-%284%29%5E3%2B3%284%29%5E2
f%284%29=-64%2B48
f%284%29=-16
so, the points are (-1,4) and (4,-16)
average rate of change is:
%28-16-4%29%2F%284-%28-1%29%29=-20%2F5=-4