5-20 Find f'(x).
5. f(x) = (3x² +6) (2x - 3)

f'(x) = 18x² - 18x + 12

Step-by-step explanation:

Differentiate using the power rule

(a ) = na

Given

f(x) = (3x² + 6)(2x - 3) ← expand factors using FOIL

     = 6x³ - 9x²  + 12x - 18 , then

f'(x) = 3.6x² - 2.9x + 12

      = 18x² - 18x + 12

maximum area = xy = (16)(32) = 512 ft2

to maximize the area of the garden, the side of the fence parallel to the side of the house should be 32 ft long, and the other two sides should both have length 16 ft.'

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