01Introduction to Derivatives - INTRODUCTION TO DERIVATIVES...

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I NTRODUCTION TO D ERIVATIVES Tangent Slope as a Function/Differentiation So what happens if you are not given the specific point at which we want to find the tangent? We can find a function to define the tangent at any point on the given curve. Let’s try finding the tangent slope at some arbitrary point. Ex . 2 ) ( x x f = at the point ) , ( 2 x x P (ie. an arbitrary point) A different point Q on the graph has coordinates ( 29 2 ) ( , h x h x + + . 0 h x x h h x h h x h xh x h x h x slopeofPQ h h h h 2 ) 0 ( 2 ) 2 ( lim 2 lim ) ( ) ( lim ) ( lim 0 2 2 2 0 2 2 0 0 = + = + = - + + = - + = Therefore the slope of the function 2 ) ( x x f = at the point ) , ( 2 x x P is x 2 , another function. This is because the slope of the function changes as the value of x changes. We call this function the derivative of ) ( x f . We denote this ) ( x f f prime x ”. In the example, the derivative of 2 ) ( x x f = is x x f 2 ) ( = . The process of calculating the derivative of a function is called
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01Introduction to Derivatives - INTRODUCTION TO DERIVATIVES...

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