Relations Functions

Let f(x) = min{2x2, 52 − 5x}, where x is any positive real number. Then the maximum possible value of f(x) is

Answer

f(x) = min{2x2, 52 − 5x}

The maximum possible value of this function is attained when 

2x2 = 52 − 5x

2x2 + 5x − 52 = 0

(2x + 13)(x − 4) = 0

=> x = −13/2 or x = 4

Since x has to be positive integer, you can discard the case when x = −13/2.

So, x = 4 is the point at which the function attains the maximum value.

Putting x = 4 in the original function,

2x2 = 32

The maximum value of f(x) = 32.

The correct answer is 32.