Differentiation: General Applications
http://www.maa.org/taxonomy/term/40457/0
enWalking with a Slower Friend
http://www.maa.org/programs/faculty-and-departments/classroom-capsules-and-notes/walking-with-a-slower-friend
<div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><p><em>Fay and Sam go for a walk. Sam walks along the left side of the street while Fay, who walks faster, starts with Sam but walks to a point on the right side of the street and then returns to meet Sam to complete one segment of their journey. The authors determine Fay’s optimal path minimizing segment length, and thus maximizing the number of times they meet during the walk. Two solutions are given: one uses derivatives; the other uses only continuity.</em></p>
</div></div></div>Minimal Pyramids
http://www.maa.org/programs/faculty-and-departments/classroom-capsules-and-notes/minimal-pyramids
<div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><p><em>The dimensions of the pyramids (with base a regular \(n\)-gon) of minimum volume containing a given sphere</em></p>
</div></div></div>Maximal Revenue with Minimal Calculus
http://www.maa.org/programs/faculty-and-departments/classroom-capsules-and-notes/maximal-revenue-with-minimal-calculus
<div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><em>A non-calculus solution to maximizing area of a rectangle inscribed in a right triangle.</em></div></div></div>A Hairy Parabola
http://www.maa.org/programs/faculty-and-departments/classroom-capsules-and-notes/a-hairy-parabola
<div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><em>Methods for maximizing a continuous function go awry when a discrete component is involved.</em></div></div></div>Maximizing the Area of a Quadrilateral
http://www.maa.org/programs/faculty-and-departments/classroom-capsules-and-notes/maximizing-the-area-of-a-quadrilateral
<div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><em>Given the lengths for four sides, the quadrilateral of maximum area is cyclic, i.e., its vertices lie on a circle.</em></div></div></div>Constrained Optimization with Implicit Differentiation
http://www.maa.org/programs/faculty-and-departments/classroom-capsules-and-notes/constrained-optimization-with-implicit-differentiation
<div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><em>Optimization of \(f(x,y)\), given the constraint \(g(x,y)=0\), can be done using implicit differentiation on both \(f(x,y)\) and \(g(x,y)=0\).</em></div></div></div>A Dozen Minima for a Parabola
http://www.maa.org/programs/faculty-and-departments/classroom-capsules-and-notes/a-dozen-minima-for-a-parabola
<div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><em>Except at the vertex, the normal to a parabola at \(P\) intersects it again at a point \(Q\). There are many interesting minimization problems generated by the line segment \(PQ\).</em></div></div></div>The Distance between Two Graphs
http://www.maa.org/programs/faculty-and-departments/classroom-capsules-and-notes/the-distance-between-two-graphs
<div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><p><em>The author shows how to use one-variable calculus to find the minimum distance between two curves.</em></p>
</div></div></div>Cable-Laying and Intuition
http://www.maa.org/programs/faculty-and-departments/classroom-capsules-and-notes/cable-laying-and-intuition
<div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><em>A familiar problem concerning cable-laying across a river may yield non-intuitive results.</em></div></div></div>Reexamining the Catenary
http://www.maa.org/programs/faculty-and-departments/classroom-capsules-and-notes/reexamining-the-catenary
<div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><em>The author describes a procedure to find the shape of the catenary formed by a chain suspended from two supports with different elevations.</em></div></div></div>Amortization: An Application of Calculus
http://www.maa.org/programs/faculty-and-departments/classroom-capsules-and-notes/amortization-an-application-of-calculus
<div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><em>The authors use the Monotonicity Theorem to prove that there is a unique monthly payment that exactly matches the amortization parameters.</em></div></div></div>The Average Distance of the Earth from the Sun
http://www.maa.org/programs/faculty-and-departments/classroom-capsules-and-notes/the-average-distance-of-the-earth-from-the-sun
<div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><p><i>Find the averages of the distances with respect to different variables.</i></p>
</div></div></div>The AM-GM Inequality via \(x^{1/x}\)
http://www.maa.org/programs/faculty-and-departments/classroom-capsules-and-notes/the-am-gm-inequality-via-x1x
<div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><p><i>A quick proof of the arithmetic-geometric mean inequality using properties of the function \(x^{1/x}\)</i></p>
</div></div></div>The Power Rule and the Binomial Formula
http://www.maa.org/programs/faculty-and-departments/classroom-capsules-and-notes/the-power-rule-and-the-binomial-formula
<div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><p><i>Using the power rule for derivatives to prove the Binomial Theorem (instead of the reverse).</i></p>
</div></div></div>An Apothem Apparently Appears
http://www.maa.org/programs/faculty-and-departments/classroom-capsules-and-notes/an-apothem-apparently-appears
<div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><p><i>Varieties of cutting a wire and forming two geometric shapes have unifying properties.</i></p>
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