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[All Steps] Honey A measure of the adhesiveness of honey that is being seeded with crystals to cause controlled crystallization can be modeled by A(g,m,s,h)=-151.78+4.26g+5.69m

Question: Honey A measure of the adhesiveness of honey that is being seeded with crystals to cause controlled crystallization can be modeled by

\[\begin{aligned} & A(g,m,s,h)=-151.78+4.26g+5.69m \\ & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,+0.67s+2.48h-0.05{{g}^{2}}-0.14{{m}^{2}}n \\ & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,-0.03{{s}^{2}}-0.05{{h}^{2}}-0.07mhn \\ \end{aligned}\]

where \(g\) is the percentage of glucose and maltose is the percentage of moisture, \(s\) is the percentage seed, and \(h\) is the holding time in days.

  1. Write functions for each of the partial derivatives of \(A\).
  2. Tell which partial derivative should be used answer the question "How quickly is adhesiveness changing as the percentage of glucose and maltose changes?"
  3. For which input variable(s) do you need a specific value in order to determine the actual rate at which adhesiveness is changing with respect the percentage moisture?
  4. Find a second partials matrix for \(A\).

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