Differentiation

Gradient function

After studying this section you should be able to:

• use differentiation to find the exact value of the gradient of a curve
• find the equation of the tangent and normal to a curve at a given point
• determine whether a function is increasing or decreasing in an interval
•  locate turning points and use the second derivative to distinguish between them

Gradient function

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• In AQA Core 1, _n will be a positive integer.
• Differentiate each term separately.
• Remember that x⁰ =1.
• When you differentiate a constant, the result is zero.

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• You cannot differentiate a product term by term.
• You cannot differentiate a quotient term by term.

Tangents and normals

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• The normal at a point is perpendicular to the tangent.

Curve sketching

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• The first two types of stationary point are also known as turning points.

The second derivative

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PROGRESS CHECK

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