Question

Find, if it exists, a value c in the interval [1, 4] such that the instantaneous rate of change of f(x) = 12 x at c is the same as the average rate of change of f over the interval [1, 4]. (If an answer does not exist, enter DNE.)

Answer 1

Answer:

c=1

Step-by-step explanation:

Given is a function as

$f(x) = 12x$

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

$f(4) = 48\\f(1) = 12\\\frac{f(4)-f(1)}{4-1} = 12$

f(c) =12 gives c =1

c lies in the interval

[1,4]

c=1 is the answer