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March 25, 2017

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f(x)=x^3-6x+1

find the critical points, where the function is increasing or decreasing and explain the shape of the graph using the derivative and algebra.

i found the derivative to be 3x^2-6. So the critical points are -1.4 and 1.4. The derivative is decreasing until (0,6) and then it begins increasing. i don't know how to go about explaining the shape of the graph with algebra though. is it related to quadratic equations???

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