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

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Given that f(x) = max{5x , 52 - 2x^{2}}, 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 - 2x^{2}

2x^{2} + 5x – 52 = 0

2x^{2} – 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 - 2x^{2} = 52 – 2(4)^{2} = 20

The minimum possible value of f(x) is 20

The question is **"Let f(x)= max{5x, 52 - 2x ^{2}}, where x is any positive real number.Then the minimum possible value of f(x) is [TITA]"**

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