Consider the function f(x) = 2/3 x^3 + bx^2 + 2x + 3, where b is some undetermined coefficient:
a) Find f ' (x) and f ''(x). f' = 2x2 + 2bx + 2f'' = 4x + 2bb) You are given that f(x) has a stationary point at x = 2. Use this information to find b.2x2 + 2bx + 2, x=2Stationary point is when f' = 02(2)2 + 2b(2) + 2 = 08 + 4b + 2 = 04b = -10b = -2.5c) Find the coordinates of the other stationary point.2x2 - 5x + 2 = 0(2x−1)(x−2)x = 0.5 or x=2Sub x = 0.5 into original function to get: (0.5 , 83/24)
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