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137 lines
5.1 KiB
HTML
137 lines
5.1 KiB
HTML
<!DOCTYPE html>
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<html lang="en"><!-- #BeginTemplate "/Templates/Advanced.dwt" --><!-- DW6 -->
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<!-- Mirrored from www.mathsisfun.com/calculus/slope-function-point.html by HTTrack Website Copier/3.x [XR&CO'2014], Sat, 29 Oct 2022 00:49:00 GMT -->
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<meta http-equiv="content-type" content="text/html; charset=UTF-8">
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<!-- #BeginEditable "doctitle" -->
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<title>Slope of a Function at a Point</title>
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<meta name="description" content="Math explained in easy language, plus puzzles, games, quizzes, worksheets and a forum. For K-12 kids, teachers and parents.">
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<script src="images/function-graph-slope.js" type="text/javascript"></script>
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<script>document.write(gTagHTML())</script>
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</head>
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<body id="bodybg" class="adv">
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<div id="stt"></div>
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<div id="adTop"></div>
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<header>
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<div id="hdr"></div>
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<div id="cookOK"></div>
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</header>
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<div class="mid">
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<nav>
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<article id="content" role="main">
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<!-- #BeginEditable "Body" -->
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<h1 class="center">Slope of a Function at a Point</h1>
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<p>Use this interactive to find the slope at a point. Instructions below.</p>
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<script>functiongraphslopeMain();</script>
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<!--<div class="flash">
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<script>putFlash6(620,550,'images/calculus-func-slope.swf','','#FFFFFF');</script>
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<noscript>
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<object type="application/x-shockwave-flash" width="620" height="550" data="images/calculus-func-slope.swf" align="middle">
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<param name="allowScriptAccess" value="sameDomain" /><param name="allowFullScreen" value="true" /><param name="movie" value="images/calculus-func-slope.swf" /><param name="quality" value="high" /><param name="bgcolor" value="#FFFFFF" /></object>
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</noscript><br>
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<a href="javascript:FlashPHP(930,825,'images/calculus-func-slope.swf','#FFFFFF')">View Larger</a>
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</div>-->
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<h2>Instructions</h2>
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<p>Type your function into the top box ... your function is plotted live.</p>
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<p>Now drag the points "A" and "B" to the function line. When they are close they will "snap" to the function.</p>
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<p>Bring points "A" and "B" near the point where you want to find the slope.</p>
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<table align="center" width="90%" border="0">
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<tbody>
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<tr>
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<td>
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<p>When "A" and "B" are on top of each other <b>the slope could be anything</b>!</p>
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<p>So keep them a small distance apart.</p></td>
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<td> </td>
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<td><img src="images/slope-function-close.gif" alt="points too close" height="52" width="190"></td>
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</tr>
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</tbody></table>
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<table align="center" width="90%" border="0">
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<tbody>
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<tr>
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<td><span class="larger"><img src="images/slope-function-zoom.gif" alt="zoom in to points" height="96" width="148"></span></td>
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<td> </td>
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<td>
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<p><span class="larger">Now Zoom In</span>: by pressing "Fit".</p>
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<p>Now bring the points <i>closer </i>together.</p></td>
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</tr>
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</tbody></table>
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<p>Keep zooming and moving the points closer together until you are happy with the answer.</p>
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<p>This is the idea behind <a href="derivatives-introduction.html">differential calculus</a>. We can't have a gap of zero (the slope could be anything), but as the <b>gap heads towards zero</b>, the slope heads towards the true slope at that point.</p>
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<h2>Interesting Functions</h2>
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<p>Try finding the slope of <span class="large">y = x^2</span> at:</p>
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<ul>
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<li>x = 1</li>
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<li>x = 2</li>
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<li>x = 3</li>
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</ul>
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<p>Try finding the slope of <span class="large">y = ln(x)</span> at:</p>
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<ul>
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<li>x = 1</li>
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<li>x = 1.5</li>
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<li>x = 2</li>
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</ul>
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<p>Try finding the slope of <span class="large">y = e^x</span> at:</p>
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<ul>
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<li><b>y</b> = 1 (x=0)</li>
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<li><b>y</b> = 1.2</li>
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<li><b>y</b> = 1.5</li>
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</ul>
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<h2>Accuracy</h2>
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<p>There are only a few hundred pixels in either direction, and so the calculations are not totally accurate. But they should give you a good feel for what is going on.</p>
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<p>And don't worry, you can often use <b>differential calculus</b> to find an accurate answer!</p>
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<p> </p>
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<div class="related">
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<a href="index.html">Calculus Index</a>
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</div>
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