Installation erforderlicher Pakete (falls nötig)

install.packages(“ggplot2”)

install.packages(“patchwork”)

# Funktionen definieren
f_a <- function(x) -x^3 + 6*x
f_b <- function(x) (1/12)*x^4 - (1/2)*x^2
f_c <- function(x) -(1/6)*x^4 + x^3 - 2*x^2
f_d <- function(x) exp(x) - 2*x^2

# Daten für Plots erstellen
x_a <- seq(-3, 3, length.out = 1000)
x_b <- seq(-3, 3, length.out = 1000)
x_c <- seq(-1, 4, length.out = 1000)
x_d <- seq(-2, 3, length.out = 1000)

# Plot für Funktion a
plot_a <- ggplot(data.frame(x = x_a, y = f_a(x_a)), aes(x, y)) +
  geom_line(color = "blue", linewidth = 1) +
  geom_point(aes(x = 0, y = 0), color = "red", size = 3) +  # Wendepunkt
  geom_point(aes(x = sqrt(2), y = 4*sqrt(2)), color = "green", size = 3) +  # Hochpunkt
  geom_point(aes(x = -sqrt(2), y = -4*sqrt(2)), color = "orange", size = 3) +  # Tiefpunkt
  geom_abline(slope = 6, intercept = 0, linetype = "dashed", color = "gray") +  # Wendetangente
  labs(title = "a) f(x) = -x³ + 6x", x = "x", y = "y") +
  theme_minimal() +
  geom_hline(yintercept = 0, color = "black", linewidth = 0.5) +
  geom_vline(xintercept = 0, color = "black", linewidth = 0.5)

# Plot für Funktion b
plot_b <- ggplot(data.frame(x = x_b, y = f_b(x_b)), aes(x, y)) +
  geom_line(color = "blue", linewidth = 1) +
  geom_point(aes(x = 0, y = 0), color = "green", size = 3) +  # Hochpunkt
  geom_point(aes(x = sqrt(3), y = -0.75), color = "orange", size = 3) +  # Tiefpunkt
  geom_point(aes(x = -sqrt(3), y = -0.75), color = "orange", size = 3) +  # Tiefpunkt
  geom_point(aes(x = 1, y = -5/12), color = "red", size = 3) +  # Wendepunkt
  geom_point(aes(x = -1, y = -5/12), color = "red", size = 3) +  # Wendepunkt
  labs(title = "b) f(x) = ¹/₁₂x⁴ - ¹/₂x²", x = "x", y = "y") +
  theme_minimal() +
  geom_hline(yintercept = 0, color = "black", linewidth = 0.5) +
  geom_vline(xintercept = 0, color = "black", linewidth = 0.5)

# Plot für Funktion c
plot_c <- ggplot(data.frame(x = x_c, y = f_c(x_c)), aes(x, y)) +
  geom_line(color = "blue", linewidth = 1) +
  geom_point(aes(x = 0, y = 0), color = "green", size = 3) +  # Hochpunkt
  geom_point(aes(x = 1, y = -7/6), color = "red", size = 3) +  # Wendepunkt
  geom_point(aes(x = 2, y = -8/3), color = "red", size = 3) +  # Wendepunkt
  labs(title = "c) f(x) = -¹/₆x⁴ + x³ - 2x²", x = "x", y = "y") +
  theme_minimal() +
  geom_hline(yintercept = 0, color = "black", linewidth = 0.5) +
  geom_vline(xintercept = 0, color = "black", linewidth = 0.5)

# Plot für Funktion d
plot_d <- ggplot(data.frame(x = x_d, y = f_d(x_d)), aes(x, y)) +
  geom_line(color = "blue", linewidth = 1) +
  geom_point(aes(x = 0, y = 1), color = "purple", size = 3) +  # y-Achsenabschnitt
  geom_point(aes(x = 0.36, y = 1.17), color = "green", size = 3) +  # Hochpunkt (approx)
  geom_point(aes(x = 2.15, y = -0.67), color = "orange", size = 3) +  # Tiefpunkt (approx)
  geom_point(aes(x = log(4), y = 0.16), color = "red", size = 3) +  # Wendepunkt
  labs(title = "d) f(x) = eˣ - 2x²", x = "x", y = "y") +
  theme_minimal() +
  geom_hline(yintercept = 0, color = "black", linewidth = 0.5) +
  geom_vline(xintercept = 0, color = "black", linewidth = 0.5)

# Alle Plots zusammen anzeigen
combined_plot <- plot_a + plot_b + plot_c + plot_d + 
  plot_layout(ncol = 2, nrow = 2)

print(combined_plot)

# Legende
legend_text <- "
Farblegende:
🔴 Rot = Wendepunkt
🟢 Grün = Hochpunkt
🟠 Orange = Tiefpunkt
🟣 Lila = y-Achsenabschnitt
--- = Wendetangente
"

cat(legend_text)