The minimum value of f(8) - f(3) is 20.
The maximum value of f(8) - f(3) is 25.
In the question, we are given that, 4 ≤ f'(x) ≤ 5 for all values of x.
Taking the given inequality as (i).
We are asked to find the minimum and maximum possible values of f(8) - f(3).
We multiply (i) by dx throughout, to get:
4dx ≤ f'(x)dx ≤ 5dx.
To find this, we integrate (i) in the definite interval [8, 3] with respect to dx, to get:
Thus, the minimum value of f(8) - f(3) is 20.
The maximum value of f(8) - f(3) is 25.
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