1 The graph of a polynomial function is given fx 49 x3 2x2

1. The graph of a polynomial function is given.

f(x) = 4/9 x^3 - 2x^2

Find coordinates of all local extrema.

local maximum (x,y) = ______

local minimum (x,y) = ______

solution

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Given that f(x) = (4/9 )x^3 - 2x^2

derivative of f(x)=(4/3)x^2-4x

critical points x=0,3

local maximum (x,y) = (0,0)

local minimum (x,y) = (3, -6)