Find the x- value of all points where the function below has any relative extrem

Question

Find the x- value of all points where the function below has any relative extrema. Find the value(s) of any relative extrema. G(x) = - x3 + 5x2 + 8x + 2 choice. The relative minima are . (Simplify your answer. Use integers or fractions for any numbers in the expression. Type an ordered pair Use a comma to separate answers as needed.) There is no solution. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. The relative maxima are . (Simplify your answer. Use integers or fractions for any numbers in the expression. Type an ordered pair. Use a comma to separate answers as needed.) There is no solution

Explanation / Answer

G ' (x) = -3x2 + 10x + 8 Local min/max when G'(x) = 0 -3x2 + 10x + 8 = 0   ------->    (-3x - 2)(x - 4) = 0   ----->   x = -2/3 or x = 4 Use test values between each critical point: G ' (-1) is negative G ' (0) is positive G ' (5) is negative So, there is a local min at x = -2/3 and a local max at x = 4 We also need the values G(-2/3) = -22/27 G(4) = 50 Therefore the relative minima are (-2/3, -22/27) and the relative maxima are (4, 50)

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