What are the local extrema, if any, of #f(x)= –2x^3 + 6x^2 + 18x –18#?

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What are the local extrema, if any, of #f(x)= –2x^3 + 6x^2 + 18x –18#?

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Answer 1 · 2016-03-22T05:08:24

Maximum f is #f(5/2)# = 69.25. Minimum f is #f(-3/2)# = 11.25.

Explanation:

#d/dx(f(x))=-6x^2+12x+18 = 0#, when # x =5/2 and -3/2#

The second derivative is #-12x+12=12(1-x) < 0# at #x = 5/2# and > 0 at x = #3/2#.
So, f(#5/2#) is the local (for finite x) maximum and f(#-3/2#) is the local (for finite x) minimum.

As #xto oo, fto -oo# and as #xto-oo, fto+oo#..

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What are the local extrema, if any, of #f(x)= –2x^3 + 6x^2 + 18x –18#?

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Explanation:

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