From: Andrew Lorimer <andrew@lorimer.id.au>
Date: Tue, 2 Apr 2019 03:35:36 +0000 (+1100)
Subject: [spec] add table of graphs for points of inflection
X-Git-Tag: yr12~172
X-Git-Url: https://git.lorimer.id.au/notes.git/diff_plain/2800efac76831ca7c242568e156cd5757f1026db?ds=sidebyside;hp=-c

[spec] add table of graphs for points of inflection
---

2800efac76831ca7c242568e156cd5757f1026db
diff --git a/spec/calculus.md b/spec/calculus.md
index c9a364e..5c3b3fc 100644
--- a/spec/calculus.md
+++ b/spec/calculus.md
@@ -194,15 +194,16 @@ $$\therefore y \implies {dy \over dx} \implies {d({dy \over dx}) \over dx} \impl
 
 Order of polynomial $n$th derivative decrements each time the derivative is taken
 
-### Maxima and minima
+### Points of Inflection
 
-- if $f^\prime (a) = 0$ and $f^{\prime\prime}(a) > 0$, then point $(a, f(a))$ is a local min (curve is concave up)
+*Point of inflection* - point of maximum gradient (either +ve or -ve). Occurs where $f^{\prime\prime} = 0$
 
+- if $f^\prime (a) = 0$ and $f^{\prime\prime}(a) > 0$, then point $(a, f(a))$ is a local min (curve is concave up)
 - if $f^\prime (a) = 0$ and $f^{\prime\prime} (a) < 0$, then point $(a, f(a))$ is local max (curve is concave down)
 - if $f^{\prime\prime}(a) = 0$, then point $(a, f(a))$ is a point of inflection
 - - if also $f^\prime(a)=0$, then it is a stationary point of inflection
 
-*Point of inflection* - point of maximum gradient (either +ve or -ve)
+![](graphics/second-derivatives.png)
 
 ## Antidifferentiation
 
diff --git a/spec/graphics/second-derivatives.png b/spec/graphics/second-derivatives.png
new file mode 100644
index 0000000..3323f40
Binary files /dev/null and b/spec/graphics/second-derivatives.png differ