If f(1) = 13 and f '(x) ≥ 3 for 1 ≤ x ≤ 3, how small can f(3) possibly be?
1 answer:
Answer:
The answer to this question is 19.
Step-by-step explanation:
Given that :
f(x)=13.
f'(x)=3. 1 ≤ x ≤ 3.
Integrate
∫f'(x) dx=∫3 dx
f(x)=3x+c 1 ≤ x ≤ 3.
f(1)= 3+c
c=13-3 =10.
f(x)=3x+10 1 ≤ x ≤ 3.
now ,
f(3)=3(3)+10=19.
So f(3) is at least 19.
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