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