1. Consider the function g(x): = -2x 1+x (a) Find the first and second derivatives of...

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1. Consider the function g(x): = -2x 1+x² (a) Find the first and second derivatives of g(x). (b) Find and classify all stationary points of g(x). Give exact values and an approximation to 2 decimal places for each point. (c) Find any points of inflection of g(x) showing a change in concavity on either side. Give exact values and an approximation to 2 decimal places for each point. (d) Graph the curve y = g(x) showing stationary points and points of inflection. (e) Hence, determine the global maximum and minimum of g(x) on the domain -∞ ≤ x < +∞o, giving exact values and an approximation to 2 decimal places for each point. 1. Consider the function g(x): = -2x 1+x² (a) Find the first and second derivatives of g(x). (b) Find and classify all stationary points of g(x). Give exact values and an approximation to 2 decimal places for each point. (c) Find any points of inflection of g(x) showing a change in concavity on either side. Give exact values and an approximation to 2 decimal places for each point. (d) Graph the curve y = g(x) showing stationary points and points of inflection. (e) Hence, determine the global maximum and minimum of g(x) on the domain -∞ ≤ x < +∞o, giving exact values and an approximation to 2 decimal places for each point.