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SarcasticallyDances
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Which points are the best approximations of the relative maximum and minimum of the function?


f(x)= x³+3x²-9x-8

AThe relative maximum is at (3, -13) and the relative minimum is at (-3, -19)
BThe relative maximum is at (-3, 19) and the relative minimum is at (1, -13)
CThe relative maximum is at (3, -13) and the relative minimum is at (3, -19)
DThe relative maximum is at (-3, -19) and the relative minimum is at (-1, -13)

Verified Answer :

HomertheGenius

f ( x ) = x³ + 3 x² - 9 x - 8We have to derive this function:f ` ( x ) = 3 x² + 6 x - 93 x² + 6 x - 9 = 0   /:3x² + 2 x - 3 = 0x² + 3 x - x - 3 = 0x ( x + 3 ) - 1 · ( x + 3 ) = 0( x + 3 ) · ( x - 1 ) = 0x1 = - 3,  x2 = 1f max = f ( - 3 ) = - 27 + 27 +27 - 8 = 19f min = f ( 1 ) = 1 + 3 - 9 - 8 = - 13Answer:B ) The relative maximum is at ( - 3 , 19 ) and the relative minimum is at ( 1 , - 13 ).
 

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