Differentiation: General Applications
https://maa.org/taxonomy/term/40457/all
enA Note on the Brachistochrone Problem
https://maa.org/programs/faculty-and-departments/classroom-capsules-and-notes/a-note-on-the-brachistochrone-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>Construction of the shortest time solution for the falling object under gravity</i></p>
</div></div></div>Maximal Revenue with Minimal Calculus
https://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 Differentiation Test for Absolute Convergence
https://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>Critical Points of Polynomial Families
https://maa.org/programs/faculty-and-departments/classroom-capsules-and-notes/critical-points-of-polynomial-families
<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 graphing calculators or computers to discuss critical points of polynomials</i></p>
</div></div></div>Minimal Pyramids
https://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 Rental Car Problem
https://maa.org/programs/faculty-and-departments/classroom-capsules-and-notes/the-rental-car-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>How to minimize the cost of filling up a rental car</i></p>
</div></div></div>The AM-GM Inequality via \(x^{1/x}\)
https://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 Pen and the Barn
https://maa.org/programs/faculty-and-departments/classroom-capsules-and-notes/the-pen-and-the-barn
<div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><I>In the classical problem of fixed perimeter and maximum area of the calculus, it is shown that the length of the fence affects the shape of the optimal pen.</I></div></div></div>The Power Rule and the Binomial Formula
https://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>Halley's Gunnery Rule
https://maa.org/programs/faculty-and-departments/classroom-capsules-and-notes/halleys-gunnery-rule
<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 author solves the classical problem of firing a projectile through a target situated on an inclined plane.</i></p>
</div></div></div>An Apothem Apparently Appears
https://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>
</div></div></div>Area and Perimeter, Volume and Surface Area
https://maa.org/programs/faculty-and-departments/classroom-capsules-and-notes/area-and-perimeter-volume-and-surface-area
<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 derivatives, the author shows the relationship in space between the volume and the surface area and in the plane between area and the perimeter.</i></p>
</div></div></div>Snapshots of a Rotating Water Stream
https://maa.org/programs/faculty-and-departments/classroom-capsules-and-notes/snapshots-of-a-rotating-water-stream
<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>Trace the trajectory of a stream of water as the nozzle rotates upward in a vertical plane.</i></p>
</div></div></div>Maximizing the Arclength in the Cannonball Problem
https://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>A Paradoxical Paint Pail
https://maa.org/programs/faculty-and-departments/classroom-capsules-and-notes/a-paradoxical-paint-pail
<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 new can, this one bounded, again has the property of having a finite volume, but an infinite surface area.</i></p>
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