I need help find all the turning points of this function:
f(x) = x^(14)-12x^(13)-21x^(12)+744x^(11)-1326x^(10)-16800x^(9)+56862x^(8)+153768x^(7)-817347x^(6)-253652x^(5)+4829511x^(4)-3026448x^(3)-9283680x^(2)+5702400x+7776000
the 14th degree polynomial is the expanded one. Here is the original one:
f(x) = (x+1)^(2)(x-5)^(3)(x+4)^(4)(x-3)^(5)
What i want to know is that, how can i find the turning points. I want to know how you can find all the turning points of this function. If you could show, can you please list all the working out, please!