2_2__Techniques_of_Differentiation

2_2__Techniques_of_Differentiation - MAC 2233 Techniques of...

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MAC 2233 Techniques of Differentiation Section 2.2 h In section 2.1 we learned that the derivative, written f’(x), is simply the slope of a tangent line. h Using h x f h x f h ) ( ) ( lim 0 + we can find the slope of any function at any given x-value. h But what if the function was 25 42 95 99 100 4 3 4 ) ( x x x x x x f + + = ? Finding h x f h x f h ) ( ) ( lim 0 + would be quite a task!! h In this section we will look at shortcuts to finding the derivative (slope of the tangent line formula) without having to use h x f h x f h ) ( ) ( lim 0 + . Techniques to finding the derivative 1. If a function ) ( x f is a constant function, i.e. ) ( x f = # (it is a horizontal line), then the derivative is zero, . 0 ) ( ' = x f h This should make sense since the slope of a horizontal line is 0 everywhere.
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Examples. Find f’(x) for the following: i. f(x) = 2 f’(x) = 0 ii. f(x) = -1/2 f’(x) = 0 iii. f(x) = 0.234 f’(x) = 0 iv. f(x) = π f’(x) = 0 2. Functions that can be
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2_2__Techniques_of_Differentiation - MAC 2233 Techniques of...

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