updates

quarto/derivatives/mean_value_theorem.qmd

@@ -330,26 +330,35 @@ Let $f(x)$ be differentiable on $(a,b)$ and continuous on $[a,b]$. Then there ex
 This says for any secant line between $a < b$ there will be a parallel tangent line at some $c$ with $a < c < b$ (all provided $f$ is differentiable on $(a,b)$ and continuous on $[a,b]$).
 
 
-This graph illustrates the theorem. The orange line is the secant line. A parallel line tangent to the graph is guaranteed by the mean value theorem. In this figure, there are two such lines, rendered using red.
+Figure @fig-mean-value-theorem illustrates the theorem. The orange line is the secant line. A parallel line tangent to the graph is guaranteed by the mean value theorem. In this figure, there are two such lines, rendered using red.
 
 
 ```{julia}
 #| hold: true
 #| echo: false
+#| label: fig-mean-value-theorem
 f(x) = x^3 - x
 a, b = -2, 1.75
 m = (f(b) - f(a)) / (b-a)
 cps = find_zeros(x -> f'(x) - m, a, b)
 
-p = plot(f, a-1, b+1,         linewidth=3, legend=false)
-plot!(x -> f(a) + m*(x-a),  a-1, b+1,   linewidth=3, color=:orange)
+p = plot(f, a-0.75, b+1,
+         color=:mediumorchid3,
+         linewidth=3, legend=false,
+         axis=([],false),
+         )
+
+
+plot!(x -> f(a) + m*(x-a),  a-1, b+1,   linewidth=5, color=:royalblue)
 scatter!([a,b], [f(a), f(b)])
 annotate!([(a, f(a), text("a", :bottom)),
            (b, f(b), text("b", :bottom))])
 
+
 for cp in cps
-    plot!(x -> f(cp) + f'(cp)*(x-cp), a-1, b+1, color=:red)
+    plot!(x -> f(cp) + f'(cp)*(x-cp), a-1, b+1, color=:brown3)
 end
+
 scatter!(cps, f.(cps))
 subsscripts = collect("₀₁₂₃₄₅₆₇₈₉")
 annotate!([(cp, f(cp), text("c"*subsscripts[i], :bottom)) for (i,cp) ∈ enumerate(cps)])