X 2 f 2 y 20 so we have x y 2 20

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Unformatted text preview: Set 04 Solution 2.7 Derivative as a rate of change 2.8 Derivative as a function 5x 2 − 20 5 x 2 + 20 x − 3 f ( x ) − f (a ) x − 3 () m = lim = = x →a x−a x−2 ( x − 2) ( x − 3) lim f ( x ) − f (a ) 3x − 3 3x + 3 = x x →1 x−a x −1 3x + 3 3x − 3 3( x − 1) = = ( x − 1) 3x + 3 ( x − 1) 3x + 3 m= ( = m= ) ( ) = 3 ( 3x + 3 lim x →1 ) ( 3x + 3 x→2 ) = 3 We need to find the point (x, y ) in order to use the point slope form. x = 2 ⇒ f (2) = y = −20 , so we have (x, y ) = (2 − 20 ) 3 a. f ( x ) = x − 2 x at P = (1, −1) Solution: You can use the power rule to differentiate the derivative: slope = f ' ( x) = 3 x 2 − 2 x =1 = 1 . You € 3 f (a + h ) − f (a ) (1 + h) − 2 (1 + h) + 1 m = lim = lim h→0 h→0 h h 2 (1 + 2 h + h ) (1 + h ) − 2 − 2 h + 1 = h h 3 + 3h 2 + h = lim = h 2 + 3h + 1 h→0 h m =1 f (x) = 5x 2 x −3 m = −2 7. The marginal profits of a company (in $/piece) can be described by the function: 2 at y = −0.01(x − 50) + 20 , where x is the number of pieces, and y is the marginal profit. a. Find...
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