## Learn Curve Sketching using Calculus techniques. A common application of derivatives.

Curve sketching allows us to see the graph of a function which can help understand its nature. Curve sketching can be easily performed using a graphing utility. However, sketching the graph of a function manually is a common question type for Calculus students. At first it seems like a complex process but, with practice, students realise it is very procedural for most functions. Any questions about this video drop us a message HERE.

## Key Points

Curve sketching refers to sketching the graph of a function

Curve sketching relies on finding key points on the graph of a function

Key points include the X & Y intercepts and the stationary points

The X intercept is found by letting y = 0 and solving the resulting equation

The Y intercept is found by letting x = 0 and solving the resulting equation

Stationary points are found by setting the derivative equal to zero and solving the equation

The ‘nature’, or type, of stationary point is determined using a nature table or 2nd derivative

The key points should fit together on the sketch to produce a coherent graph

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