CAT 2018 Functions Question (Hard)

Question

Let where is a positive real number. Then maximum possible value of ?

Accepted Answer

Step 1 We are given two functions increasing with and decreasing with To maximize the minimum of the two, equate them Rewriting Step 2 Use the quadratic formula So, the positive root is Step 3 At Since both expressions are equal at , this is the point where the minimum is maximized. Final Answer The

CAT 2018

Quantitative

Functions

Hard

Let $f(x) = \min\{2x^2,\ 52 - 5x\}$ where $x$ is a positive real number. Then maximum possible value of $f(x)$ ?

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