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Test the function g(x)=−8x^3−(−300)x^2+(−3600)x−5 for relative maximum and minimum. Use the second-derivative test if possible.?
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- 7 years ago
g(x)=−8x^3−(−300)x^2+(−3600)x−...
g'(x) =- 24x^2+600x-3600. For minima or maxima, g'(x) = 0
-24x^2+600x-3600=0
x^2-25x+150 = 0
(x-15)(x-10) = 0
so at x = 15 and x= 10 either maxima or minima occurs.
to find the maxima or minima
g"(x) = -48x+600
plugging x = 15 and 10, we get g"(x) = -120 and 120 respectively.
SO THE FUNCTION HAS MAXIMA AT X = 15 AND MINIMA AT X=10
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