69 lines
1.9 KiB
HTML
69 lines
1.9 KiB
HTML
{% extends "layout.html" %}
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{% block title %}
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Differentiated
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{% endblock %}
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{% block main %}
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<div class="col-sm-12" style="background-color: #0f11175c; padding: 20px">
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<font color="white" size="5">
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<div>
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<p>Your function is $f(x) = {{ value }}$</p>
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<p>Your Linear Approximation of $f(x)$ at $x = {{ h }}$ is ${{ lh }}$</p>
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</div>
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</font>
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</div>
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<font color="white">
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<table class="table" action="optimized">
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<tbody>
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<tr class="bg-dark text-white">
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<td>Step 1</td>
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<td>Setup L(x)</td>
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</tr>
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<tr class="table-secondary">
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<td></td>
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<td>$L(x) = f({{ a }}) + f'({{ a }})(x-{{ a }})$</td>
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</tr>
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<tr class="bg-dark text-white">
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<td>Step 2</td>
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<td>Take the Derivative</td>
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</tr>
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<tr class="table-secondary">
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<td></td>
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<td>$f'(x) = {{ fprime }}$</td>
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</tr>
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<tr class="bg-dark text-white">
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<td>Step 3</td>
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<td>Plug in values</td>
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</tr>
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<tr class="table-secondary">
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<td></td>
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<td>$f({{ a }}) = {{ fa }}$</td>
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</tr>
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<tr class="table-secondary">
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<td></td>
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<td>$f'({{ a }}) = {{ fprimea }}$</td>
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</tr>
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<tr class="table-secondary">
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<td></td>
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<td>$L(x) = {{ fa }} + [{{ fprimea }}(x - {{ a }})]$</td>
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</tr>
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<tr class="bg-dark text-white">
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<td>Step 4</td>
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<td>Use our $L(x)$ to approximate $f({{ h }})$</td>
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</tr>
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<tr class="table-secondary">
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<td></td>
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<td>$L({{ h }}) = {{ fa }} + [{{ fprimea }}({{ h }} - {{ a }})]$</td>
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</tr>
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<tr class="table-secondary">
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<td></td>
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<td> $= {{ lh }}$</td>
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</tr>
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</tbody>
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</table>
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</font>
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<img src={{url}} alt='Chart' height='500' width='500'>
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{% endblock %}
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