SOLUTION: Find the interval(s) where the function f(x)=x^3-4x+2 is decreasing. For me to better understand this problem I think I would benefit from understanding the method behind solving t
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Question 993814: Find the interval(s) where the function f(x)=x^3-4x+2 is decreasing. For me to better understand this problem I think I would benefit from understanding the method behind solving this equation and all the information related to solving of this problem. I appreciate all your help and would greatly appreciate a -step-by-step system for solving to fully understand this porblem and other similar porblems. Thank you. Answer by rothauserc(4718) (Show Source):
You can put this solution on YOUR website! we use the first derivative of f(x) = x^3 -4x +2
I assume f(x) is continuous on an interval I and differentiable on the interior of I, then if first derivative is < 0 for all x belonging to I, then f(x) is decreasing on I
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first derivative of f(x) = x^3 -4x +2 is
f'(x) = 3x^2 - 4
therefore f(x) is decreasing on the open interval (-4/3, 4/3)
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here is the graph of f(x) = x^3 -4x +2 to help visualize the solution
