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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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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