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QUESTION 3 Given the function f ( x ) = X - X a) Find the x and y intercept b) Find the interval of increasing and decreasing c) Find the interval of concavity d) Sketch the graph. a) Find the x -intercept and y-intercept. For x-intercept y = 0, substitute y = 0 or f(x) = 0 in Find f'(x) - differentiate f(x) f(x) Find x - intercept From result first step, solve x, Let f'(x) =0 Answer 1) Find Critical point. Solve x (from equation 2) For y - intercept x = 0, substitute x = 0 in equation of Find y or f(x) for value of x from 3) f(x Find y - intercept From result first step, solve x 2) Set up interval from critical point and test for Answer. first derivative. And make conclusion. Find f"(x) - differentiate f(x) twice Let f"(x) =0 1) Find Inflection point Solve x (from equation 2) Find y or f(x) for value of x from 3) 2) Set up interval from inflection point and test for second order derivative. And make conclusion