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ZanzabumX [31]
3 years ago
5

Let the function f be continuous and differentiable for all x. Suppose you are given that f(−1)=−3, and that f'(x) for all value

s of x. Use the Mean Value Theorem to determine the largest possible value of f(5).

Mathematics
1 answer:
Monica [59]3 years ago
8 0

Answer:

Step-by-step explanation:

By MVT,

f'(c) = \frac{f(5)-f(-1)}{5-1}

4f'(c)= f(5) + 3\rightarrow f(5) = 4f'(c) - 3

Moreover, f'(x)\leq 4~~~~~~ \forall x,

f(5) \leq 16 - 3 =13

Hence the largest possible value of f(5) is 13

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