Option 1: Identify the max and make your color vector
set.seed(47)
n <- 1e4
xx <- runif(n)
yy <- rexp(n)
colors <- rep("black", n)
colors[which.max(yy)] <- "red"
plot(xx, yy, col = colors, pch = 16)
Option 2: Plot the max separately. This is probably easier, especially if you want to adjust more characteristics than just color.
plot(xx, yy, pch = 16)
points(xx[which.max(yy)], yy[which.max(yy)], col = "red", pch = 17, cex = 2)