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If f(2) = 13 and f '(x) ≥ 2 for 2 ≤ x ≤ 7, how small can f(7) possibly be?​

User Shaneil
by
8.2k points

1 Answer

3 votes

Answer:

23

Explanation:

We are given that

f(2)=13


f'(x)\geq 2


2\leq x\leq 7

We have to find the possible small value of f(7).

We know that


f'(x)=(f(b)-f(a))/(b-a)

Using the formula


f'(x)=(f(7)-f(2))/(7-2)


f'(x)=(f(7)-13)/(5)

We have


f'(x)\geq 2


(f(7)-13)/(5)\geq 2


f(7)-13\geq 2* 5


f(7)-13\geq 10


f(7)\geq 10+13


f(7)\geq 23

The small value of f(7) can be 23.

User Yadhu Babu
by
7.6k points

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