Updated version of https://gist.github.com/andrewheiss/29057150cc6466f0f4d9c39236c19aa6 . It has three main changes: 1) Model variables are swapped for convenience, 2) Adding tangent line wrapped into function with extra functionality, 3) Plot is done for a new model with swapped variables and then coordinates are flipped.

upgraded_sideways_polynomial_tangents.R

library(tidyverse)
library(Deriv)
library(scales)

# Here we change variable names: x is "Work effort", y is "Wage per hour"
response_curve <- function(x) 60*x^4 + 5*x + 6
response_deriv <- Deriv(response_curve)

# Function for tangent line becomes very simple. For more information, see:
# https://en.wikipedia.org/wiki/Tangent#More_rigorous_description
response_tangent <- function(x, effort) {
  response_curve(effort) + response_deriv(effort) * (x - effort)
}

add_tangent <- function(effort, x_width = 0.25, y_width = 15) {
  # Compute the x limits which will be used to plot tangent line. It is computed
  # as minimum of simmetrical intervals (with `effort` in the middle) which
  # give the input plotting width along x and y axis.
  half_plot_width_x <- 0.5 * x_width
  # This is computed from the following equation:
  # `abs(g(effort + d) - g(effort)) = 0.5 * y_width` (here `g` is
  # `response_tangent` and `d` is what we're looking)
  half_plot_width_y <- 0.5 * y_width / abs(response_deriv(effort))
  half_plot_width <- min(half_plot_width_x, half_plot_width_y)
  x_lim <- effort + half_plot_width * c(-1, 1)
  
  # Return a `stat_function()` output wrapped in the list so that we can use it
  # as "normal" 'ggplot2' layer function
  list(
    stat_function(
      fun = response_tangent, args = list(effort = effort),
      color = "darkred", size = 1, xlim = x_lim
    )
  )
}

response_curve_points <- tibble(x = seq(0, 1, 0.01)) %>% 
  mutate(y = response_curve(x))

ggplot(data = tibble(x = c(0, 1)), aes(x = x)) + 
  # Add polynomial curve
  geom_line(data = response_curve_points, aes(x = x, y = y), 
            size = 0.5, color = "grey30") +
  # Add tangent lines
  add_tangent(effort = 0.5) +
  add_tangent(effort = 0.25) +
  add_tangent(effort = 0.8) +
  # Add dots at tangent points
  annotate(geom = "point", x = 0.5, y = response_curve(0.5)) +
  annotate(geom = "point", x = 0.25, y = response_curve(0.25)) +
  annotate(geom = "point", x = 0.8, y = response_curve(0.8)) +
  # Labels and scale stuff
  labs(x = "Work effort from employee", y = "Wage per hour") +
  scale_x_continuous(labels = percent_format(accuracy = 1), expand = c(0, 0)) +
  scale_y_continuous(labels = dollar, expand = c(0, 0)) +
  # The main trick: plot of inverse function is made by straightforward
  # coordinate flipping
  coord_flip(xlim = c(0, 1), ylim = c(0, 50)) +
  theme_minimal()