If f(1) = 13 and f '(x) ≥ 3 for 1 ≤ x ≤ 3, how small can f(3) possibly be?

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.

the correct option is 2.

step-by-step explanation:

according to the given information triangle abc is a right angle triangle with right angle at a. segment ab is 5 and segment ac is 7. point d is on segment bc and angles adb and adc are right angles.

it is given that triangles abd, cad, and cba are similar.

two triangles are similar if their corresponding sides are proportional.

in triangle cba, using pythagoras theorem

                      )

triangle abd and cba are similar,

                            (2)

triangle cad and cba are similar,

                      )

using (1), (2) and (3), we get

hence proved.

therefore option 2 is correct.