Question 865758
Graph it first to get some idea.
{{{graph(300,300,-3,3,-100,100,6x^6-x^5+7x^4+x^3-9x^2+9x-6
)}}}
No maxima but to find the minima, find the derivative and set it equal to zero.
{{{36x^5-5x^4+28x^3+3x^2-18x+9=0}}}
{{{graph(300,300,-2,2,-2,2,36x^5-5x^4+28x^3+3x^2-18x+9
)}}}
The value of x when the derivative is zero (minima occurs) is {{{x=-0.774}}}