Let f(x) = min {2x2, 52 − 5x}, where x is any positive real number. Then the maximum possible value of f(x) is
Explanation:
For positive value of x, (2x2) is increasing.
As value of x increases, value of (52 – 5x) decreases.
Since, these 2 functions are continuously increasing and decreasing respectively, the max value of f(x) will occur when both these functions are equal.
i.e. 2x2 = 52 − 5x, for x = 4 and − 6.5
At x = 4, function attains maximum value for positive real value of x.
∴ at x = 4, f(x) = 32
Hence, 32.
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