f[x_] := (12*x^5 + 15*x^4 - 260*x^3 + 720*x)/60

p1 := Plot[f[x], {x, -6, 4}, PlotRange -> All]

p2 := Plot[f'[x], {x, -6, 4}, PlotRange -> All]

Show[p1, p2];

Solve[f'[x] == 0.0, x]

f[-6] // N

f[-4.03749]

f[-0.95933]

f[1.0521]

f[2.94473]

f[4] // N