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<p>In calculus, the second derivative decides whether a critical point of <em>y</em>(x) is a minimum. For functions of multiple variables, the test is whether a matrix of second derivatives is positive definite. In this session we learn several ways of testing for positive definiteness and also how the shape of the graph of <em>ƒ</em>(x) = x<em><sup>T</sup></em> <em>A</em>x is determined by the entries of <em>A</em>.</p>
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<p><a href="/assets/courseware/v1/f19d9772598450a3c269d108f6436ccb/asset-v1:OCW+18.06SC+2T2019+type@asset+block/18.06_Unit_III_3.3_Lectrans.pdf" target="[object Object]">Lecture video transcript (PDF)</a></p>
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<h2 class="hd hd-2 unit-title">Lecture Summary and Reading</h2>
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<h3>Lecture Summary</h3>
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<h3>Suggested Reading</h3>
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<ul>
<li>Read Section 6.5 in the 4<sup>th</sup> or 5<sup>th</sup> edition. </li>
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<p>Work the problems on your own and check your answers when you're done.</p>
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