How do you find the instantaneous rate of change for #f(x)= 3sqrtx# for [4,25]?

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Answer 1 · 2016-03-08T03:26:25

#3/{2sqrtx}#

The instantaneous rate of change is defined for each point, not in an interval. We say

"What is the instantaneous rate of change of #f(x)# at #x=4#?"

not

"What is the instantaneous rate of change of #f(x)# for #4<=x<=25#?"

unless you are asking for all the values in that interval. Usually people ask for average rate of change in an interval.

To find the instantaneous rate of change, differentiate.

#f'(x) = 3/{2sqrtx}#

That's it. If you want to know the instantaneous rate of change at say at #x=16#, just plug it in.

#f'(16) = 3/{2sqrt16} = 3/8#