# BCH2(rev) - CH 2 Differentiation 1 Derivative P y = f(x...

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CH 2 - Differentiation 1. Derivative Problem Find the slope of the tangent to the curve y = f ( x ) at P ( a , f ( a )). y = f ( x ) P

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The slope of PQ = tan θ The slope of the tangent to the curve y = f ( x ) at P ( a , f ( a )) is :
The derivative of f at ‘ x = a = = the slope of the tangent to the curve y = f ( x ) at a the slope of y = f ( x ) at a the ( instantaneous ) rate of change of ywrtx at a h a f h a f h ) ( ) ( lim 0 +

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Given f ( x ) = x ³ , show that ( x ) = 3 x ²
Let f ( x ) = x . Show: (0) doesn’t exist

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Equivalent Form By letting x = a + h , we have : h a f h a f h ) ( ) ( lim 0 +
Differentiability Let f : D . If a is in D & ( a ) exists, say : f is differentiable at ‘ a ’. If f is differentiable at every a ’in D , say : f is differentiable on D .

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Geometrical Meaning •The existence of f ´ ( a ) is a smoothness condition on the curve y = f ( x ) at ‘ a ’.