SOLUTION: Find the equations of the tangent to the curve y = x(x - 2)(x - 4) at the origin. Show that this tangent is parallel to the tangent at the point where x = 4 ( and not at the point
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-> SOLUTION: Find the equations of the tangent to the curve y = x(x - 2)(x - 4) at the origin. Show that this tangent is parallel to the tangent at the point where x = 4 ( and not at the point
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Question 1121469: Find the equations of the tangent to the curve y = x(x - 2)(x - 4) at the origin. Show that this tangent is parallel to the tangent at the point where x = 4 ( and not at the point x = -4 Found 2 solutions by greenestamps, ikleyn:Answer by greenestamps(13195) (Show Source):
Find the derivative of the function and evaluate it at x=0, at x=4, and x=-4. Show that the derivatives (slopes of the graph) at x=0 and x=4 are the same and the derivative at x=-4 is different.
Note: expanding the given expression into a polynomial will make finding the derivative MUCH easier....
You can put this solution on YOUR website! .
Find the equations of the tangent to the curve y = x(x - 2)(x - 4) at the origin. Show that this tangent is parallel
to the tangent at the point where x = 4 ( and not at the point x = -4
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Look into the plot of the function (of the polynomial) y = x(x - 2)(x - 4).
Notice that it is anti-symmetrical about the point (x,y) = (2,0).
Therefore, it is not so amazing that the tangent to the curve at the origin x= 0 is the same as the tangent at the point x= 4.
