You can get the answer by taking the derivative of the function.

y'=6x^2+6x-180=x^2+x-30=(x-5)(x+6)

let y'>0, function is increasing at x>5, x<-6

let y'<0, function is decreasing at -6<x<5

let y'=0, we get the critical point, x=5, x=-6.

By looking at the graph, or analyze from the increasing/decreasing of the function above, we get local maximum at x=-6, local minimum at x=5

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