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If f(2) = 5 and f '(x) ≥ 1 for 2 ≤ x ≤ 6, how...

If f(2) = 5 and f '(x) ≥ 1 for 2 ≤ x ≤ 6, how small can f(6) possibly be?

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Answer #1

If f is continuous on [a,b] and differentiable on (a,b) then according to mean value theorem there exists c in (a,b) such that,

Let's assume that f is continuous on [2,6] and differentiable on (2,6) then according to mean value theorem there exists c in (2,6) such that,

Hence we can say that,

we have f(2) = 5 hence,

The smallest value of f(6) possibly be 9

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