90 lines
1.8 KiB
Plaintext
90 lines
1.8 KiB
Plaintext
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#import "/src/lib.typ" as functastic
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#set page(width: auto, height: auto)
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#functastic.sign-table(
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($-oo$, $-1$, $x_0$, $1$, $3$, $+oo$),
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espcl: 2.6,
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{
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import functastic: *
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sign-line(
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$f_7'(x)$,
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(none, $-$, "d", $-$, "t", $-$, "d", "h", "d", $+$, none)
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)
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sign-line(
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$f_7''(x)$,
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(none, $-$, "d", $+$, $0$, $-$, "d", "h", "d", $-$, none)
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)
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func-line(
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$f_7(x)$,
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mult: 2,
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(
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val(asymp($y=-1$), "top"),
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disc(($-oo$, "bottom"), ($+oo$, "top")),
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none,
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disc(center: ($0$, "bottom"), eod: true),
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disc(center: ($0$, "bottom")),
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val(asymp($y=1$), "top"),
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inter($y_0$, 2, 4, i: 2)
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)
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)
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convex-line(
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"concavité",
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mult: 2,
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(
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none,
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false,
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"AV",
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true,
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"PI",
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false,
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none,
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none,
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none,
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false,
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none
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)
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)
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}
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)
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#pagebreak()
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#functastic.sign-table(
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($-oo$, $-sqrt(2)/2$, $(3 - sqrt(5))/4$, $sqrt(2)/2$, $1$, $(3 + sqrt(5))/4$, $+oo$),
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espcl: 2.5,
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{
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import functastic: *
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sign-line($f'(x)$, (none, $-$, "d", "h", none, "h", "d", $-$, $0$, $+$, "t", $+$, none))
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sign-line($f''(x)$, (none, $-$, "d", "h", none, "h", "d", $+$, "t", $+$, $0$, $-$, none))
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func-line($f(x)$, mult: 2, (
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val(asymp($-2sqrt(2)$), "top"),
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disc(($-oo$, "bottom"), eod: true),
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disc(eod: true),
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disc(right: ($+oo$, "top")),
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val($2$, "bottom"),
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none,
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val(asymp($2sqrt(2)$), "top"),
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inter($(2sqrt(1 + sqrt(5))) / sqrt(3)$, 3, 4, i: 5)
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))
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convex-line("concavité", (
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none,
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false,
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"AV",
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none,
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none,
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none,
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"AV",
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true,
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none,
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true,
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"PI",
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false,
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none
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))
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}
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)
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