# L11 - interval if Where is the above function...

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L11 – The Derivative The slope of the tangent line to a curve y = f ( x ) at x = a , if it exists, is denoted as It is called the of the function f at x = a . The equation of the tangent line at x = a is 1

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Find the equation of the tangent line to f ( x ) = x 2 - 2 x + 1 at (3 , 4). 2
In general, the derivative as a function is f 0 ( x ) = Other notation: Other interpretations Process of ﬁnding the derivative is called Domain of f 0 ( x ) is 3

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Given the graph of f ( x ), sketch a possible graph of the derivative. 4
Find f 0 ( x ) if f ( x ) = x 2 - x and state the domain. 5

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Def – A function f is diﬀerentiable at a if f 0 ( a ) exists. It is diﬀerentiable on an

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Unformatted text preview: interval if Where is the above function diﬀerentiable? 6 Find f (1) if f ( x ) = x 2 x > 1 2-x x ≤ 1 Sketch f ( x ) and ﬁnd a formula for f ( x ). What do you note about continuity and diﬀerentiability at x = 1? 7 Thm – If f is diﬀerentiable at a , then f is continuous at a . 8 When is a function not diﬀerentiable? 9 A graph of f ( x ) has a vertical tangent line when Find f (-1) if f ( x ) = ( x + 1) 1 3 . 10...
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L11 - interval if Where is the above function...

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