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# A company determines that if $x$ thousand dollars are spent on advertising a certain product, then $S(x)$ units of the product will be sold, where$S(x)=-2 x^3+27 x^2+132 x+207 \quad 0 \leq x \leq 17$a. Sketch the graph of $S(x)$.b. How many units will be sold if nothing is spent on advertising?c. How much should be spent on advertising to maximize sales? What is the maximum sales level?

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We know:

Point c is relative maximum if $f'(x)>0$ to left and $f' (x)<0$ on right of point c.

Point c is relative minimum if $f'(x)<0$ to left and $f'(x)>0$ on right of point c.

Point c is not relative extremum if both sides have the same sign.

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