Discussion 15 Q12.3.5

In Exercises 5 – 8, evaluate fx(x, y) and fy(x, y) at the indicated point. 5. f(x, y) = x2y − x + 2y + 3 at (1, 2)

# Define the function
f <- function(x, y) {
  return(x^2 * y - x + 2 * y + 3)
}

# Define partial derivatives
fx <- function(x, y) {
  return(2 * x * y - 1)
}

fy <- function(x, y) {
  return(x^2 + 2)
}

x_value <- 1
y_value <- 2

fx_at_point <- fx(x_value, y_value)
fy_at_point <- fy(x_value, y_value)

# Print the results
cat("f_x(1, 2) =", fx_at_point, "\n")

## f_x(1, 2) = 3

cat("f_y(1, 2) =", fy_at_point, "\n")

## f_y(1, 2) = 3