ANSWERS: 1

Given f'(x)≥2 for 1≥x≥4, then f(x) will be bounded below by the line y = 2x + c for some constant c. Since we are looking for a lower bound for f(4), this would be achieved by having f(x) = 2x + c for the identified interval. All that is now required to resolve the question is to derive the value for c, which we are able to do given that f(1) = 8: 8 = f(1) = 2(1) + c 8 = 2 + c c = 6 Therefore, we have f(x) = 2x + 6, upon which f(4) = 2(4) + 6 = 14, or f(4) = 14 (the smallest possible value)
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