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How to Use a Negative Tangent

The tangent to a curve is a line that touches a curve at only one point. The tangent moves in the same direction as the curve at that point. Using tangents aids in determining a line's slope at a given point. While a curve's slope may change from point to point, the tangent line's slope at a point has a constant slope. Therefore, a tangent line's slope at a point is equal to the curve's slope at that point. Negative tangents help in determining the regions of a graph that have negative slopes, granting insight into the graph's behavior in those regions.

Instructions

- 1
  Identify the points on a graph that have negative tangents. Use them to create a new curve that graphically represents the magnitude of the negative slope of the curve at those points.
- 2
  Calculate numerous negative tangent values along the curve of the graph of a function.
- 3
  Plot the negative tangent values on a separate coordinate grid. Make each x-coordinate equal to the x-coordinate of the original function and each y-coordinate equal to the tangent value at the point.
- 4
  Draw a smoothly curved line connecting each of the negative tangent points on the graph. The resulting graph displays the magnitude of the slope at each point on the original function.

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