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  3. given function g(x)= 8x^3 - 108x^2 + 480x, find th

Given function g(x)= 8x^3 - 108x^2 + 480x, find the first derivative, g'(x)____________Notice that g'(x)...

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Calculus

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Given function g(x)= 8x^3 - 108x^2 + 480x, find the first derivative, g'(x)____________Notice that g'(x) = 0 when x = 4, that is, g'(4) = 0.Now, we want to know whether there is a local minimum or local maximum at = 4, so we will use the second derivative test.Find the second derivative, g''(x).g''(x)_______________Evaluate g''(4)g''(4)=_________________Based on the sign of this number, does this mean the graph of g(x) is concave up or concave down at= 4?[Answer either up or down -- watch your spelling!!]At x= 4 the graph of g(x) is concave_____________Based on the concavity of g(x) at x = 4, does this mean that there is a local minimum or local maximum at x= 4?[Answer either minimum or maximum -- watch your spelling!!)At = 4 there is a local____________

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