Applications of Differentiation (HSC SSCE Mathematics Advanced): Flashcards

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Applications of Differentiation
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Point-gradient formula

y−y1=m(x−x1)y - y_1 = m(x - x_1)

Normal gradient if tangent gradient is mm

- rac{1}{m}

Relationship between normal and tangent lines

Perpendicular

If y′′<0y'' < 0 at stationary point, nature is

Maximum

If y′′>0y'' > 0 at stationary point, nature is

Minimum

Stationary points occur when

First derivative equals zero

Inflection points occur where

Second derivative changes sign

Derivative of sin⁡x\sin x

cos⁡x\cos x

Derivative of cos⁡x\cos x

−sin⁡x-\sin x

y=asin⁡x+bcos⁡xy = a\sin x + b\cos x produces what shape?

Wave with modified amplitude and phase shift

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