Let f(x)=ln(3x)+2.5 . what is the average rate of change of f(x) from 2 to 7? round your answer to the nearest hundredth.

For this case what we should do is evaluate the function in each of the points from 2 to 7 and then find the average.
 We have then:
 f (x) = ln (3x) +2.5.
 f (2) = ln (3 * 2) + 2.5 = 4.291759469
 f (3) = ln (3 * 3) + 2.5 = 4.697224577
 f (4) = ln (3 * 4) + 2.5 = 4.98490665
 f (5) = ln (3 * 5) + 2.5 = 5.208050201
 f (6) = ln (3 * 6) + 2.5 = 5.390371758
 f (7) = ln (3 * 7) + 2.5 = 5.544522438
 Then the average is:
 Average = (4.291759469 + 4.697224577 + 4.98490665 + 5.208050201 + 5.390371758 + 5.544522438) / (6) = 5.019472516
 nearest hundredth
 5.02
 
 the average rate of change of f (x) from 2 to 7 is  5.02

The average rate of change of is .

Given,

.

We have to calculate the average rate of change, from varies to .

So, we calculate the value of at and calculate the average.

How to calculate the average rate?

Here at ,

So,

.

Similarly,

Again,

Again,

Again,

Again,

Now Average Rate of change of from 2 to 7 will be,

.

On rounding it off to the nearest hundredth the average rate of change of is .

Hence the average rate of change of is .

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