Suppose that f(x) is continuous and differentiable on the interval [2,5]. Suppose also that f(2) = 9 and f’(x) ≤9. What is the largest possible value for f(5)?
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Expert's answer
2011-03-10T09:53:32-0500
We'll try to use the definition of the derivative: f'(x) = (f(b) - f(a))/(b-a)) thus (f(5) - f(2))/(5-2) = (f(5) - 9) /3 ≤ 9. (f(5) - 9) ≤ 27 f(5) ≤ 36. Answer: 36.
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