Curve Sketching

Essential Features of a Curve Sketch

Sketching curves requires some essential features to be shown, which include:

  • Y-Intercepts (where x=0)

  • X-Intercepts (where y=0)

  • Co-Ordinates of Stationary Points (determined using the first derivative test)

  • Nature of the Stationary Points (determined using the second derivative test)

After you have all this information, you should be able to sketch a curve by connecting the ponts.


Worked Example 1: Curve Sketch from Equation

In this example, we are given the following question.

Step 1: Determine X-Intercepts and Y-Intercepts

Step 2: Determine Stationary Points

Applications of Differentiation

Step 3: Determine the Nature of the Stationary Points

Note: You may have sufficient information in step 2 to skip step 3.

Step 4: Join the Dots

Use the nature of the stationary points to think about how the co-ordinates would connect.

Below is the finished sketch of the equation y=x^3-3x


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