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Analyze the polynomial function f(x)-x3+x22x- Answer parts (a) through.docx
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### Find the relative extrema of the function, if they exist. List the ex.pdf

1. Find the relative extrema of the function, if they exist. List the extremum along with the x-value at which it occurs. G(x) = x^3 - 5x^2 - 8x - 3 1) Identify all the realtive minima. Select the correct choice below and if neccessary fill in the box to complete your choice. a. The relative minima are (_________ , ___________) **Simplify your answer. Use intergers or fractions for any numbers in the expression. Type an ordered pair. Use a comma to seperate answers as needed.**** b. There are no relative minima. 2) Identify all the relative maxima. Select the correct choice below and if neccessary fill in the box to complete your choice. a. The relative maxima are (____________ , _____________)**Simplify your answer. Use intergers or fractions for any numbers in the expression. Type an ordered pair. Use a comma to seperate answers as needed.**** b. There are no relative maxima. Solution Relative minimum if g'(x) = 0 and g''(x)>0 Relative maximum if g'(x) = 0 and g''(x)<0 g'(x) = 3x^2 - 10x -8 = 0 x = 4 or -2/3 g''(x) = 3x -10 g''(4) = 2 >0 g''(-2/3) = -12 So, g has a relative minimum at 4 and relative maximum at -2/3
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