A process to extract pectin and p ment from sunflower heads nvolves unflower whe

Question

A process to extract pectin and p ment from sunflower heads nvolves unflower when the water temperature is i shing the sunfi er heads in heated water. A model or the percentag of pigment that can be removed from sun w er head by washing or 20 minutes in?milliliters o water per gram o PlT, r}-306.761-9.6544T + 1.9836r + 0.0736872-0,02958,2 percent, . (a) Locate the critical pcint af the pigment removal function. (Round yours answers to three decimal places.) the point in part la) as a relative maximum, a relative minimum, or a saddle point O relative maximun relative minimum saddle paint

Explanation / Answer

Let f be a function with two variables with continuous second order partial derivativesfxx, fyy and fxy at a critical point (a,b). Let

D = fxx(a,b) fyy(a,b) - fxy2(a,b)

If D > 0 and fxx(a,b) > 0, then f has a relative minimum at (a,b).

If D > 0 and fxx(a,b) < 0, then f has a relative maximum at (a,b).

If D < 0, then f has a saddle point at (a,b).

If D = 0, then no conclusion can be drawn.

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