What is the average rate of change of function f given by f(x)=x^4-5x on the closed interval [0,3]?
2007-05-06 14:12:09 · 5 answers · asked by Anonymous in Science & Mathematics ➔ Mathematics
f(0)=0
f(3)=3^4-5*3
=81-15
=66
points (0,0) and (3,66)
Average rate of change is slope of straight line between these points
or (66-0)/(3-0) = 22
Average rate of change is 22
2007-05-06 14:28:44 · answer #1 · answered by gudspeling 7 · 0⤊ 0⤋
f(0)=0^4-5*0=0-0=0
f(3)=3^4-5*3=81-15=66
From (0,0) to (3,66) the slope is 66/3 = 22.
The average rate of change is 22.
I forgot to much to give the instantaneous rate for any given x.
2007-05-06 14:19:56 · answer #2 · answered by STEVEN F 7 · 0⤊ 0⤋
Take the first derviative and evaluate for x=0 and x=3. Average the 2 answers.
2007-05-06 14:18:15 · answer #3 · answered by Scott H 3 · 0⤊ 1⤋
f(0)=0
f(3)=66
66-0 / 3-0 = 22
2007-05-06 14:20:33 · answer #4 · answered by Jeff M 3 · 0⤊ 0⤋
x^5/5-5x^2/2 is the integral
(3^5/5-5*3^2/2)/3=8.7
2007-05-06 14:17:59 · answer #5 · answered by bruinfan 7 · 0⤊ 2⤋