GATE 2022 IN – Question 28
The global minimum of $x^3e^{-|x|}$ for $x\in(-\infty,\infty)$ occurs at $x=$ ______ (one decimal place).
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Correct answer: -3.0 to -3.0
Explanation
For x<0, f=x³eˣ and f′=eˣx²(x+3). It decreases before −3 and increases after −3, attaining a negative minimum there. For x≥0 the function is nonnegative, while tails approach zero.
Thus **x=−3.0**.