If f(4) = 4 and f '(x) geq 2 for 4 leq x leq 7, how small can f(7) possibly be?

abondantQ

abondantQ

Answered question

2021-02-23

If f(4)=4 and f(x)2 for 4x7, how small can f(7) possibly be?

Answer & Explanation

unessodopunsep

unessodopunsep

Skilled2021-02-24Added 105 answers

Assuming that the function is continuous on the interval [4,7][4,7], you could use the mean value theorem.
For x(4,7)x(4,7), one has by the mean value theorem that :
f(x)=(7)432
So that
f(7)10
ie the smallest value that f(7) can obtain is 10.

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