Describe the graph of the function f (x) = x3 - 11x2 + 36x - 36. Include the y-intercept, x-intercepts, and the shape of the graph.

Hello,

f (x) = x^3-11x²+36x-36

y-intercept

x=0==>y=-36

x-intercepts

f (2) = 2^3-11*4+72-36=8-44+36=0

f (x) = (x-2) (x²-9x+18)

g (x) = x²-9x+18

g (3) = 3²-9*3+18=0

g (x) = (x-3) (x-6)

f (x) = (x-2) (x-3) (x-6)

f' (x) = 3x²-22x+36 = (x - (11+√13) / 3) (x - (11-√13) / 3)

x≈4,8685 ... or x≈9,7981