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jverzani
2024-05-22 07:55:20 -04:00
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quarto/limits/intermediate_value_theorem.qmd
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@@ -86,7 +86,7 @@ Suppose we have a continuous function $f(x)$ on $[a,b]$ with $f(a) < 0$ and $f(b
We use this fact when building a "sign chart" of a polynomial function. Between any two consecutive real zeros the polynomial can not change sign. (Why?) So a "test point" can be used to determine the sign of the function over an entire interval.
Here, we use the Bolzano theorem to give an algorithm - the *bisection method* - to locate the value $c$ under the assumption $f$ is continous on $[a,b]$ and changes sign between $a$ and $b$.
Here, we use the Bolzano theorem to give an algorithm - the *bisection method* - to locate the value $c$ under the assumption $f$ is continuous on $[a,b]$ and changes sign between $a$ and $b$.
```{julia}
@@ -603,7 +603,7 @@ The output of `find_zeros` is a vector of values. To check that each value is an
f₁.(zs)
```
(For a continuous function this should be the case that the values returned by `find_zeros` are approximate zeros. Bear in mind that if $f$ is not continous the algorithm might find jumping points that are not zeros and may not even be in the domain of the function.)
(For a continuous function this should be the case that the values returned by `find_zeros` are approximate zeros. Bear in mind that if $f$ is not continuous the algorithm might find jumping points that are not zeros and may not even be in the domain of the function.)
### An alternate interface to `find_zero`