# Suppose that 2 ≤ f '(x) ≤ 4 for all values of x. What are the minimum and maximum possible values of f(5) − f(3)?

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cosinusix | Certified Educator

Integrate the given inequalities between 3 and 5.

`int_3^5 2dxlt=int_3^5f'(x)dxlt=int_3^5 4d x`

`4lt=f(5)-f(3)lt=8 `

f(5)-f(3) is between 4 and 8.

f(5)-f(3) can be 4 is f'(x) is constant, equal to 2

f(5)-f(3) can be 8 is f'(x) is constant equal to 4

**Therefore the minimum possible value of f(5)-f(3) is 4.**

**The maximum possible value of f(5)-f(3) is 8.**