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

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): You can put this solution on YOUR website!

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....
Answer by ikleyn(52754)   (Show Source): 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
~~~~~~~~~~~~~~~~~~

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.

        Plot y =

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