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How do you find the points where the graph of the function #y=3x# has horizontal tangents and what is the equation?

Answer 1

Evelyn Agard

No such points exist.

#y=3x# is the equation of a straight line with slope #=3# at all points on the line.

To have a horizontal tangent, the equation would have to have a slope of #0# at the tangent point.

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Answer 2

Luke Alvarez

To find the points where the graph of the function y=3x has horizontal tangents, we need to determine the values of x that make the derivative of the function equal to zero.

The derivative of y=3x is given by dy/dx = 3.

Setting dy/dx equal to zero, we have 3 = 0.

However, this equation has no solution since 3 is not equal to zero.

Therefore, the graph of the function y=3x does not have any points where it has horizontal tangents.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.