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) = 6x + 11x6/11 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) = 6 + 6x-5/11 local min/max when G '(x) = 0 or undefined. Undefined at x = 0   G(0) = 0 G'(x) = 0   ----->   x-5/11 = -1   ----->   x = -1   G(-1) = 5 Take test values between each critical value to determine if they are min or max G'(-2) is positive G'(-0.5) is negative G'(1) is positive Therefore, there are relative minima at (0,0) and relative maxima at (-1,5) local min/max when G '(x) = 0 or undefined. Undefined at x = 0   G(0) = 0 G'(x) = 0   ----->   x-5/11 = -1   ----->   x = -1   G(-1) = 5 Take test values between each critical value to determine if they are min or max G'(-2) is positive G'(-0.5) is negative G'(1) is positive Therefore, there are relative minima at (0,0) and relative maxima at (-1,5)

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