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  1. What is the relative maximum and minimum of the function?

f(x)=x^3+3x^2-24x

AThe relative maximum is at (4, 28) and the relative minimum is at (-2, -80).
BThe relative maximum is at (-4, 80) and the relative minimum is at (2, -28).
CThe relative maximum is at (4, 80) and the relative minimum is at (-2, -28).
DThe relative maximum is at (-4, 28) and the relative minimum is at (2, -80).
  1. Classify -2x^4 - x^3 + 8x^2 + 12 by degree.
Aquintic
Bquartic
Ccubic
Dquadratic

Verified Answer :

apologiabiology

take the derititve

f'(x)=3x^2+6x-24
set to zero
0=3(x^2+2x-8)
0=3(x-2)(x+4)
at x=2 and -4

those are where the min and max are

ok so
sign chart
to the lft of -4, the sign is positive
betweeen -4 and 2, the sign is negative
tothe right of 2 the sign is positive


max=sign changef from (+) to (-)
min=sign change from (-) to (+)

so max at x=-4 and min at x=2

find x=2, the value is -28

answer is C










2. 4th degree so quartic (qua, like quad or quadrilatal)

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