Tangent

numderiv(f, x₀, ϵ = 1e-7)

Returns the approximate numerical derivative of $f(x)$ at $x_0$ using the forward finite-difference method with a step $\epsilon$. Namely:

$f'(x_0) \approx \frac{f(x_0 + \epsilon) - f(x_0)}{\epsilon}$

Examples

julia> f(x) = x^2
f (generic function with 1 method)

julia> numderiv(f, 3, 1e-2)
6.009999999999849

julia> numderiv(f, 3, 1e-4)
6.000100000012054

plottangent(f, x₀, xs, ϵ=1e-7)

Plots the approximate tangent of $f(x)$ at $x_0$.

tangent(f, x₀, ϵ = 1e-7)

Returns the approximate tangent of $f(x)$ at $x_0$, as a function of x, namely:

$r(x) = f'(x_0) \cdot (x - x_0) + f(x_0)$