# Find the coordinates of the points on the graph of #y=3x^2-2x# at which tangent line is parallel to the line #y=10x#?

Two lines are parallel if they share the same slope.

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To find the coordinates of the points on the graph of y=3x^2-2x at which the tangent line is parallel to the line y=10x, we need to determine the derivative of the function y=3x^2-2x.

The derivative of y=3x^2-2x is given by dy/dx = 6x - 2.

Since the tangent line is parallel to the line y=10x, their slopes must be equal. Therefore, we set the derivative equal to the slope of the line y=10x, which is 10.

6x - 2 = 10

Solving this equation, we find x = 2.

To find the corresponding y-coordinate, we substitute x=2 into the original equation y=3x^2-2x:

y = 3(2)^2 - 2(2)

Simplifying, we get y = 12 - 4 = 8.

Therefore, the coordinates of the points on the graph of y=3x^2-2x at which the tangent line is parallel to the line y=10x are (2, 8).

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