

Curve Sketching
Essential Features of a Curve Sketch
Sketching curves requires some essential features to be shown, which include:
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Y-Intercepts (where x=0)
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X-Intercepts (where y=0)
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Co-Ordinates of Stationary Points (determined using the first derivative test)
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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