Has a Horizontal Tangent?

A horizontal tangent line is a mathematical feature on a graph, located where a function's derivative is zero. ... Horizontal lines have a slope of zero. Therefore, when the derivative is zero, the tangent line is horizontal.

How do you find where a function has a horizontal tangent?

To find the points at which the tangent line is horizontal, we have to find where the slope of the function is 0 because a horizontal line's slope is 0. That's your derivative. Now set it equal to 0 and solve for x to find the x values at which the tangent line is horizontal to given function.

At what points does the curve have a horizontal tangent?

The curve will have a horizontal tangent line only when the above is equal to zero. Clearly, the fraction can be zero only when the numerator is equal to zero: 0=3x2 + 2x = x(3x + 2).