Answer:
c=1
Step-by-step explanation:
Given is a function as
[tex]f(x) = 12x[/tex]
We have to find mean value theorem in the interval [1,4] and find c such that f(c) = average rate of change
We find that f is both differentiable and continuous in the given interval
[tex]f(4) = 48\\f(1) = 12\\\frac{f(4)-f(1)}{4-1} = 12[/tex]
f(c) =12 gives c =1
c lies in the interval
[1,4]
c=1 is the answer
