Question

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

Answer 1

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