test_values <- seq(from = 2, to = 4, by = 0.001)
product <- sapply(test_values, function(x) x^(100/x))
library(ggplot2)
ggplot(data.frame(test_values, product)) + aes(x = test_values, y = product) +
geom_line() + theme_classic() + scale_x_continuous(breaks = c(2, exp(1),
3, 4), labels = c("2", expression(e), "3", "4"), name = "base") + scale_y_continuous(breaks = c()) +
ggtitle("product obtained when taking a base to the power of its division into 100\n") +
geom_vline(xintercept = exp(1), linetype = "dotted")