f(5) = 20

f′(5) = 2 <-- the function is increasing at this point

f′′(x) < 0, x ≥ 5 <-- the function is concave down from at least 5 to ∞

The value of the derivative shows how fast this is growing, 2 units y per 1 unit x at x = 5. Concave down on the given interval means the function will increase to a point then start decreasing again. We can infer from the derivative that

f(6) ≈ 22

f(7) ≈ 24

The farther we move away from initial derivative, however, the less accurate it is. From the low value of the derivative and the concavity it can be inferred that 26 is impossible for f(7).

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