a continuous function f has domain (1,25) and range (3,30). if f'(x) is less than 0 for all x between 1 and 25, what is f(25)?

Question

a continuous function f has domain (1,25) and range (3,30). if f'(x) is less than 0 for all x between 1 and 25, what is f(25)?
a)1
b)3
c)25
d)30
e)impossible to determine from the information given

Reiny · Accepted Answer

draw a rectangle with vertices
(1,30), (1,3), (25,3) and (25,30)

notice domain is from 1 to 25
and the range is from 3 to 30

your graph must lie within that rectangle, and it is constantly decreasing. ( f' (x) < 0 )

Since the domain ends at 25 and the range is as low as 3,
(25,3) must be the endpoint of your graph

so f(25) = 3