CAT 2022 Functions Question (Hard)

Question

Let and . Then the maximum value of becomes 100 when is equal to

Accepted Answer

We are given 0 le a le x le 100, quad f x x-a x-100 x-a-50 We must find the value of for which maximum value of becomes 100 . --- Step 1 Analyze critical points The breakpoints of are Function is piecewise linear, so maximum will occur at endpoints or breakpoints. --- Step 2 Evaluate at breakpoints

CAT 2022

Quantitative

Functions

Hard

Let $0 \leq a \leq x \leq 100$ and $f(x)=|x-a|+|x-100|+|x-a-50|$ . Then the maximum value of $f(x)$ becomes 100 when $a$ is equal to

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