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find all points on the curve y=x^33X where the tangent is parallel to the xaxis.
 one year ago
 one year ago
find all points on the curve y=x^33X where the tangent is parallel to the xaxis.
 one year ago
 one year ago

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calculusfunctionsBest ResponseYou've already chosen the best response.2
When in doubt always start with the derivative of the function. Hence if y = x³ − 3x dy/dx = 3x² − 3 where dy/dx is of course the instantaneous rate of change function (the slope function). Since the tangent to y is parallel to the xaxis, dy/dx = 0 ∵ the slope of the xaxis is zero (xaxis is horizontal and the slope of any horizontal line is zero). Thus dy/dx = 0 and since dy/dx = 3x² − 3, 3x² − 3 = 0 solving for x, we obtain x = ±1 when x = 1, y = 2 when x = 1, y = 2 ∴ the tangent to y = 3x² − 3 is parallel to the xaxis at the points (1, 2) and (1, 2)
 one year ago
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