CAT 2020 Functions Question (Hard)

Question

For real , the maximum possible value of is

Accepted Answer

Step 1 Let , so , Alternatively, define Let To find maximum value, consider f x dx left right Use quotient rule f x cdot 1 - x cdot 2 1 x 4 -1 2 cdot 4x 3 1 x 4 Simplify numerator f x - 1 x 4 f x 1 x 4 left - right 1 x 4 cdot 1 x 4 3 2 Set derivative to 0 1 - x 4 0 Rightarrow x 1 --- Step 2 Compute

CAT 2020

Quantitative

Functions

Hard

For real $x$ , the maximum possible value of $\frac{x}{\sqrt{1 + x^{4}}}$ is

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