SOLUTION: Find the average rate of change for f(x)= -2x^2 + 5x - 2 on [-1, 1]

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: Find the average rate of change for f(x)= -2x^2 + 5x - 2 on [-1, 1]       Log On


   

Question 1114790: Find the average rate of change for f(x)= -2x^2 + 5x - 2 on [-1, 1]
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!

Explanation:
the average rate of change of f%28x%29 over an interval [a,b] is the slope+of the secant line connecting the 2 points: point (a,f%28a%29) and point (b,f%28b%29)

average rate of change =%28f%28b%29-f%28a%29%29%2F%28b-a%29

given: f%28x%29=+-2x%5E2+%2B+5x+-+2 on [-1,+1]

-> so, [a,b] = [-1,+1] => a=-1 and b=1

substitute in: average rate of change =%28f%28b%29-f%28a%29%29%2F%28b-a%29
average rate of change =%28f%281%29-f%28-1%29%29%2F%281-%28-1%29%29
find f%281%29:
+f%281%29=+-2%2A1%5E2+%2B+5%2A1+-+2=-2%2B5-2=5-4=1
find f%28-1%29:
+f%28-1%29=+-2%2A%28-1%29%5E2+%2B+5%2A%28-1+%29-+2=-2-5-2=-9
plug it in
average rate of change =%281-%28-9%29%29%2F%281-%28-1%29%29

average rate of change =%281%2B9%29%2F%281%2B1%29
average rate of change = 10%2F2
average rate of change =5