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

##### 1 Answer

Mar 8, 2016

#### Explanation:

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

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