Question

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. −3.99 −0.25 0.25 3.99

Answer 1

Choice C is correct answer.

Explanation:

We have given a function.

We have to find average rate of change of function from a to b.

Let f(x) = ln (3x) , a = 2 and b = 7

f(2) = ln(6) and f(7) = ln(21)

Derivative is defined as rate of change of function.

d/dx(f(x)) = f(b)-f(a) / (b-a)

Putting the values of a and b in above formula,we get

d/dx(f(x)) = f(7)-f(2) / 7-2

d/dx(f(x)) = ln(21)-ln(6) / 5

d/dx(f(x)) = 1.25 / 5

d/dx(f(x)) = .25

Average rate of change of function from 2 to 7 is .25

Answer 2

Rate of change is 0.25

Explanation:

The given function is
`f(x)=\ln(3x)`

The rate of change of function f(x) from a to b is given by

`f'(x)=(f(b)-f(x))/(b-a)`

We have,

a = 2, b = 7

Thus, rate of change from 2 to 7 is given by

`\text{Rate of change}=(f(7)-f(2))/(7-2)\\\\=(\ln(21)-\ln(6))/(7-2)\\\\=(1.25)/(5)\\\\=0.25`

Thus, rate of change is 0.25