Baking—Sugar Content: A pastry chef in a commercial test kitchen is fine-tuning a pie-fill...

Baking—Sugar Content: A pastry chef in a commercial test kitchen is fine-tuning a pie-filling recipe. Colleagues acting as tasters have rated various recipes on a scale of 1 to 10. The average rating f(x) can be modeled as a function of the sugar content x by

where x is the number of tablespoons of sugar in the recipe, and f(x) represents the taster rating.

(a) Graph f using the viewing window [0, 40] by [0, 10].

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(b) Evaluate f(20), f(25), and f(30), and interpret each.

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(c) Evaluate and interpret .

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(d) From the results (a), (b), and (c), how much sugar seems to be optimal?