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Question 30 : Let f(x)= max{5x, 52 - 2x²}, where x is any positive real number.Then the minimum possible value of f(x) is [TITA]

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Method of solving this CAT Question from Functions

Given that f(x) = max{5x , 52 - 2x²}, where x is any positive real number.
The minimum possible value of f(x) has to found.
The minimum possible value is obtained if the two curves intersect or
5x = 52 - 2x²
2x² + 5x – 52 = 0
2x² – 8x + 13x – 52 = 0
2x(x - 4) + 13(x - 4) = 0
(2x + 13)(x - 4) = 0
x = \\frac{-13}{2}) or 4
One of these would be the minimum possible value
It is given that x is a positive real number. So, we have to consider only when x = 4
When x = 4
5x = 5 × 4 = 20
52 - 2x² = 52 – 2(4)² = 20
The minimum possible value of f(x) is 20