From 1093dee791d26866e84e5fa262483a7f7e333134 Mon Sep 17 00:00:00 2001 From: Krasen Samardzhiev Date: Fri, 27 Feb 2026 17:06:57 +0000 Subject: [PATCH] Corrected Latex function in optimization example --- quarto/derivatives/optimization.qmd | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/quarto/derivatives/optimization.qmd b/quarto/derivatives/optimization.qmd index ce7f820..e17e8ba 100644 --- a/quarto/derivatives/optimization.qmd +++ b/quarto/derivatives/optimization.qmd @@ -699,7 +699,7 @@ Here traveling directly to the point $(L,0)$ is fastest. Though travel is slower ## Unbounded domains -Maximize the function $xe^{-(1/2) x^2}$ over the interval $[0, \infty)$. +Maximize the function $xe^{-x^2}$ over the interval $[0, \infty)$. Here the extreme value theorem doesn't technically apply, as we don't have a closed interval. However, **if** we can eliminate the endpoints as candidates, then we should be able to convince ourselves the maximum must occur at a critical point of $f(x)$. (If not, then convince yourself for all sufficiently large $M$ the maximum over $[0,M]$ occurs at a critical point, not an endpoint. Then let $M$ go to infinity.