Mathematics, 12.12.2019 23:31 bree9362
Example 5 suppose that f(0) = ā7 and f '(x) ā¤ 8 for all values of x. how large can f(3) possibly be? solution we are given that f is differentiable (and therefore continuous) everywhere. in particular, we can apply the mean value theorem on the interval [0, 3] . there exists a number c such that f(3) ā f(0) = f '(c) 3 correct: your answer is correct. ā 0 so f(3) = f(0) + 3 correct: your answer is correct. f '(c) = ā7 + 3 correct: your answer is correct. f '(c). we are given that f '(x) ā¤ 8 for all x, so in particular we know that f '(c) ā¤ 8 correct: your answer is correct. multiplying both sides of this inequality by 3, we have 3f '(c) ā¤ 24 correct: your answer is correct. , so f(3) = ā7 + incorrect: your answer is incorrect. f '(c) ā¤ ā7 + incorrect: your answer is incorrect. = incorrect: your answer is incorrect. the largest possible value for f(3) is .
Answers: 2
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Example 5 suppose that f(0) = ā7 and f '(x) ā¤ 8 for all values of x. how large can f(3) possibly be?...
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