Differentiation: General Applications
http://www.maa.org/taxonomy/term/40457/0
enA Differentiation Test for Absolute Convergence
http://www.maa.org/programs/faculty-and-departments/classroom-capsules-and-notes/a-differentiation-test-for-absolute-convergence
<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 presents an easy absolute convergence test for series based solely on differentiation, with examples.</em></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>Maximizing the Arclength in the Cannonball Problem
http://www.maa.org/programs/faculty-and-departments/classroom-capsules-and-notes/maximizing-the-arclength-in-the-cannonball-problem
<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>The article shows how to maximize the arclength of the trajectory of a cannonball.</i></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>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>