:depth: 2

```

In addition to what's in Anaconda, this lecture will require the following library:

```{code-cell} ipython

---

tags: [hide-output]

---

!pip install interpolation

```

## Overview

In this lecture we continue the study of {doc}`the cake eating problem <cake_eating_problem>`.

```{code-cell} ipython

import matplotlib.pyplot as plt

plt.rcParams["figure.figsize"] = (11, 5) #set default figure size

import numpy as np

from interpolation import interp

from scipy.optimize import minimize_scalar, bisect

```

"""

u, β = self.u, self.β

v = lambda x: interp(self.x_grid, v_array, x)

v = lambda x: np.interp(x, self.x_grid, v_array)

return u(c) + β * v(x - c)

```

"""

u, β, α = self.u, self.β, self.α

v = lambda x: interp(self.x_grid, v_array, x)

v = lambda x: np.interp(x, self.x_grid, v_array)

return u(c) + β * v((x - c)**α)

```

u_prime, β, x_grid = ce.u_prime, ce.β, ce.x_grid

σ_new = np.empty_like(σ_array)

σ = lambda x: interp(x_grid, σ_array, x)

σ = lambda x: np.interp(x, x_grid, σ_array)

def euler_diff(c, x):

return u_prime(c) - β * u_prime(σ(x - c))