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 :

\(f'(x)=\frac{(7)-4}{3}\geq2\)

So that

\(f(7)\geq10\)

ie the smallest value that f(7) can obtain is 10.

For \(x∈(4,7)x∈(4,7)\), one has by the mean value theorem that :

\(f'(x)=\frac{(7)-4}{3}\geq2\)

So that

\(f(7)\geq10\)

ie the smallest value that f(7) can obtain is 10.