Asked by Skirby
The function f(x)=-2x^3+30x^2-96x+8 has one local minimum & one local maximum. This function has a local minimum at x equals ______ with value __________ and a local maximum at x equals _______ with value __________ .
Answers
Answered by
Steve
f' = -6x^2 + 60x - 96
= -6(x^2-10x+16)
= -6(x-2)(x-8)
So, local min/max occurs where f' = 0
f" = -6(2x-10)
= -12(x-5)
f is max where f" < 0
f is min where f" > 0
Let 'er rip!
= -6(x^2-10x+16)
= -6(x-2)(x-8)
So, local min/max occurs where f' = 0
f" = -6(2x-10)
= -12(x-5)
f is max where f" < 0
f is min where f" > 0
Let 'er rip!
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