Question:
Let f(x) = min{2x2 ,52−5x}, where x is any positive real number. Then the maximum possible value of f(x) is
Let f(x) = min{2x2 ,52−5x}, where x is any positive real number. Then the maximum possible value of f(x) is
Updated On: Sep 30, 2024
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Correct Answer: 32
Solution and Explanation
f(x) = min(2x2,52-5x)
The maximum possible value of this function will be 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, we can discard the case x = -13/2
x = 4 is the point at which the function attains the maximum value.
putting x = 4 in the original function, we get, 2x2 = 2*42 = 32.
Or the maximum value of f(x) = 32
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