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.

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

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