Question

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

Answer 1

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.