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Home Continuous Functions Maxima and Minima - Applications Examples Example 3: Inscribing a Cylinder Into a Sphere Sollution Two: Implicit Differentiation | |||||||
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Sollution Two: Implicit Differentiation
Instead of eliminating h and expressing V as a function of x, we shall use the equations in their original form and find the critical points by implicit differentiation.
CONCLUSION The maximum of V is at x = h/√2. At that point the ratio of x to h is x/h = 1/√2. The second method of solution may be better in a problem where it is hard or impossible to find explicit equations for the dependent variables (like h and V) as functions of the independent variable.
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Home Continuous Functions Maxima and Minima - Applications Examples Example 3: Inscribing a Cylinder Into a Sphere Sollution Two: Implicit Differentiation |