## Related questions with answers

Question

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?

Solution

VerifiedAnswered 2 years ago

Answered 2 years ago

Step 1

1 of 8We 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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