Question 993814
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
{{{ graph( 300, 200, -3, 3, -10, 15, x^3 -4*x +2) }}}