How do you find the average rate of change of #f(x)=x^3-3x+5# over [-1,5]?

1 Answer
Alan P.
Oct 17, 2015

Find the difference in the value of the rate of change, #f'(x)#, between the two end points of the interval, then divide that difference by the interval width to get the average rate of change.

Explanation:

Given #f(x)=x^3-3x+5#
#color(white)("XXX")#Rate of change #= f'(x) = 3x^2-3#

#f'(-1) = 3(1)-3 = 0#
#f(5) = 3(25)-3 = 72#
Difference in #f'(x)# between the two end points: #Delta f_(5:-1)(x) = 72-0 = 72#

Width of interval: #Delta x= 5-(-1) = 6#

Average rate of change: #=72/6 = 12#

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