Question

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

Answer 1

Answer:

23

Step-by-step 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

$f'(x)=\frac{f(b)-f(a)}{b-a}$

Using the formula

$f'(x)=\frac{f(7)-f(2)}{7-2}$

$f'(x)=\frac{f(7)-13}{5}$

We have

$f'(x)\geq 2$

$\frac{f(7)-13}{5}\geq 2$

$f(7)-13\geq 2\times 5$

$f(7)-13\geq 10$

$f(7)\geq 10+13$

$f(7)\geq 23$

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