Merge pull request #78 from fangliu-tju/main

Update optimization.qmd

quarto/derivatives/optimization.qmd

@@ -278,7 +278,7 @@ This value is the lone critical point, and in this case gives the position of th
 ### Using `argmax` to identify where a function is maximized
 
 
-This value that maximizes a function is sometimes referred to as the *argmax*, or argument which maximizes the function. In `Julia` the `argmax(f,domain)` function is defined to "Return a value $x$ in the domain of $f$ for which $f(x)$ is maximized. If there are multiple maximal values for $f(x)$ then the first one will be found." The domain is some iterable collection. In the mathematical world this would be an interval $[a,b]$, but on the computer it is an approximation, such as is returned by `range` below. Without out having to take a derivative, as above, but sacrificing some accuracy, the task of identifying `x` for where `A` is maximum, could be done with
+This value that maximizes a function is sometimes referred to as the *argmax*, or argument which maximizes the function. In `Julia` the `argmax(f,domain)` function is defined to "Return a value $x$ in the domain of $f$ for which $f(x)$ is maximized. If there are multiple maximal values for $f(x)$ then the first one will be found." The domain is some iterable collection. In the mathematical world this would be an interval $[a,b]$, but on the computer it is an approximation, such as is returned by `range` below. Without having to take a derivative, as above, but sacrificing some accuracy, the task of identifying `x` for where `A` is maximum, could be done with
 
 
 ```{julia}
@@ -445,10 +445,10 @@ Ethan Hunt, a top secret spy, has a mission to chase a bad guy. Here is what we
   * He can drive a car - usually some concept car by BMW - at $30$ miles per hour, but only on the road.
 
 
-For his mission, he needs to go $10$ miles west and $5$ `miles north. He can do this by:
+For his mission, he needs to go $10$ miles west and $5$ miles north. He can do this by:
 
 
-  * just driving $8.310$ miles west then $5$ miles north, or
+  * just driving $10$ miles west then $5$ miles north, or
   * just running the diagonal distance, or
   * driving $0 < x < 10$ miles west, then running on the diagonal
 
@@ -846,7 +846,7 @@ Is there "symmetry" in the answer between $x$ and $y$?
 yesnoq("no")
 ```
 
-What is you were do do two pens like this back to back, then the answer would involve a rectangle. Is there symmetry in the answer now?
+What is you were to do two pens like this back to back, then the answer would involve a rectangle. Is there symmetry in the answer now?
 
 
 ```{julia}
@@ -969,7 +969,7 @@ diff(SA, x, x)(xx) > 0
 radioq((
 "This applies the second derivative test to the lone *real* critical point showing there is a local minimum at that point.",
 "This applies the first derivative test to the lone *real* critical point showing there is a local minimum at that point.",
-"This finds the ``4`th derivative of `SA`"
+"This finds the `4`th derivative of `SA`"
 ), 1)
 ```
 
@@ -1004,7 +1004,7 @@ numericq(val, 1e-3)
 ###### Question Non-Norman windows
 
 
-Suppose our new "Norman" window has half circular tops at the top and bottom? If the perimeter is fixed at $20$ and the dimensions of the rectangle are $x$ for the width and $y$ for the height.
+Suppose our new "Norman" window has half circular tops at the top and bottom. If the perimeter is fixed at $20$ and the dimensions of the rectangle are $x$ for the width and $y$ for the height.
 
 
 What is the value of $y$ that maximizes the area?
@@ -1091,7 +1091,7 @@ We approach this using `SymPy` and $n=10$
 ```{julia}
 #| hold: true
 #| eval: false
-@syms s xs[1:10]
+@syms x xs[1:10]
 s(x) = sum((x-xi)^2 for xi in xs)
 cps = solve(diff(s(x), x), x)
 ```
@@ -1274,7 +1274,7 @@ choices = ["exactly four times",
 L"exactly $\pi$ times",
 L"about $2.6$ times as big",
 "about the same"]
-answ = 1
+answ = 3
 radioq(choices, answ)
 ```
 
@@ -1390,7 +1390,7 @@ choices = ["It finds the critical points",
 radioq(choices, 1)
 ```
 
-The polynomial `nu` is what degree in `p`?
+The polynomial `eq` is what degree in `p`?
 
 
 ```{julia}
@@ -1399,7 +1399,7 @@ The polynomial `nu` is what degree in `p`?
 numericq(4)
 ```
 
-The only positive real solution for $p$ from $nu$ is
+The only positive real solution for $p$ from $eq$ is
 
 
 ```{julia}
@@ -1420,7 +1420,8 @@ In [Hall](https://www.maa.org/sites/default/files/hall03010308158.pdf) we can fi
 
 
 ```{julia}
-#| hold: true, echo
+#| hold: true
+#| echo: false
 p = plot(; legend=false, aspect_ratio=:equal, axis=nothing, border=:none)
 	b = 2.
 	plot!(p, x -> x^2, -b, b)
@@ -1471,7 +1472,7 @@ numericq(a)
 Numerically find the value of $a$ that minimizes the length of the line seqment $PQ$.
 
 
-```{juila}
+```{julia}
 #| hold: true
 #| echo: false
 x(a) = -a - 1/(2a)