HW3 - Section 3.1 1. f ( x ) = 0. (Rule 1) 3. f ( x ) = 5 x...

Info iconThis preview shows pages 1–3. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Section 3.1 1. f ( x ) = 0. (Rule 1) 3. f ( x ) = 5 x 5- 1 = 5 x 4 . (Rule 2) 5. f ( x ) = 2 . 1 x 2 . 1- 1 = 2 . 1 x 1 . 1 . (Rule 2) 7. f ( x ) = (3)( x 2 ) = (3)(2 x 2- 1 ) = 6 x 1 = 6 x. (Rules 2 and 3) 9. f ( r ) = ( )( r 2 ) = ( )(2 r 2- 1 ) = 2 r 1 = 2 r. (Rules 2 and 3) 11. f ( x ) = (9)( x 1 / 3 ) = (9)((1 / 3) x (1 / 3)- 1 ) = 3 x- 2 / 3 . (Rules 2 and 3) 13. f ( x ) = (3 x (1 / 2) ) = (3)( x 1 / 2 ) = (3)((1 / 2) x (1 / 2)- 1 ) = (3 / 2) x- 1 / 2 . (Rules 2 and 3) 15. f ( x ) = (7)( x- 12 ) = (7)(- 12 x- 12- 1 ) =- 84 x- 13 . (Rules 2 and 3) 17. f ( x ) = (5 x 2 ) +(- 3 x ) +(7) = (5)( x 2 ) +(- 3)( x ) +0 = (5)(2 x 2- 1 )+(- 3)( x 1- 1 ) = 10 x- 3 . (Rules 1, 2, 3, and 4) 19. f ( x ) = (- x 3 ) + (2 x 2 ) + (- 6) = (- 1)( x 3 ) + (2)( x 2 ) + 0 = (- 1)(3 x 3- 1 ) + (2)(2 x 2- 1 ) =- 3 x 2 + 4 x. (Rules 1, 2, 3, and 4) 21. f ( x ) = (0 . 03 x 2 ) + (- . 4 x ) + (10) = (0 . 03)( x 2 ) + (- . 4)( x 1 ) + 0 = (0 . 03)(2 x 2- 1 ) + (- . 4)( x 1- 1 ) = 0 . 06 x- . 4 . (Rules 1, 2, 3, and 4) 23. f ( x ) = ( x 3 x ) + (- 4 x 2 x ) + ( 3 x ) = ( x 2 ) + (- 4 x ) + (3 x- 1 ) = 2 x 2- 1 + (- 4)( x 1 ) + (3)( x- 1 ) = 2 x + (- 4)( x 1- 1 ) + (3)((- 1) x- 1- 1 ) = 2 x- 4- 3 x- 2 . (Rules 2, 3, and 4) 25. f ( x ) = (4 x 4 ) + (- 3 x (5 / 2) ) + (2) = (4)( x 4 ) + (- 3)( x (5 / 2) ) + 0 = (4)(4 x 4- 1 ) + (- 3)((5 / 2) x (5 / 2)- 1 ) = 16 x 3- (15 / 2) x 3 / 2 . (Rules 1, 2, 3, and 4) 27. f ( x ) = (3 x- 1 ) + (4 x- 2 ) = (3)( x- 1 ) + (4)( x- 2 ) = (3)((- 1) x- 1- 1 ) + (4)((- 2) x- 2- 1 ) =- 3 x- 2- 8 x- 3 . (Rules 2, 3, and 4) 29. f ( t ) = ( 4 t 4 ) + (- 3 t 3 ) + ( 2 t ) = (4 t- 4 ) + (- 3 t- 3 ) + (2 t- 1 ) = (4)( t- 4 ) + (- 3)( t- 3 ) + (2)( t- 1 ) = (4)(- 4 t- 4- 1 ) + (- 3)(- 3 t- 3- 1 ) + (2)(- t- 1- 1 ) =- 16 t- 5 + 9 t- 4- 2 t- 2 . (Rules 2, 3, and 4) 31. f ( x ) = (2 x ) + (- 5 x ) = (2 x ) + (- 5 x 1 / 2 ) = (2)( x ) + (- 5)( x 1 / 2 ) = (2)( x 1- 1 ) + (- 5)((1 / 2) x 1 / 2- 1 ) = 2- (5 / 2) x- 1 / 2 . (Rules 2, 3, and 4) 33. f ( x ) = ( 2 x 2 ) + (- 3 x 1 / 3 ) = (2 x- 2 ) + (- 3 x- 1 / 3 ) = (2)( x- 2 ) + (- 3)( x- 1 / 3 ) = (2)(- 2 x- 2- 1 ) + (- 3)((- 1 / 3) x (- 1 / 3)- 1 ) =- 4 x- 3 + x- 4 / 3 . (Rules 2, 3, and 4) 35. f ( x ) = (2 x 3 ) + (- 4 x ) = (2)( x 3 ) + (- 4)( x ) = (2)(3 x 3- 1 ) + (- 4)( x 1- 1 ) = 6 x 2- 4 . f (- 2) = 6(- 2) 2- 4 = 20 f (0) = 6(0) 2- 4 =- 4 f (- 2) = 6(2) 2- 4 = 20 . 41. f ( x ) = (2 x 2 ) + (- 3 x ) + (4) = (2)( x 2 ) + (- 3)( x ) + 0 = (2)(2 x 2- 1 ) + (- 3)( x 1- 1 ) = 4 x- 3 . The slope of the tangent line at the point (2,6) is f (2) = 4(2)- 3 = 5 . Thus the equation of the tangent line in slope intercept form is given by y = f (2) x + b = 5 x + b. To determine the value of b we substitute the x and y values at the point (2,6) into the equation and obtain 6 = 5(2) + b = 10 + b so that b =- 4 and the equation of the tangent line is y = 5 x- 4 ....
View Full Document

This note was uploaded on 02/14/2012 for the course MAC 2233 taught by Professor Smith during the Spring '08 term at University of Florida.

Page1 / 36

HW3 - Section 3.1 1. f ( x ) = 0. (Rule 1) 3. f ( x ) = 5 x...

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online