{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

1024worksheet7 - (a f x =(1-2 x-1(b f x = x-x 3-x 5 4(c f x...

Info iconThis preview shows pages 1–10. Sign up to view the full content.

View Full Document Right Arrow Icon
Polytechnic Institute of NYU MA 1024/1324 Worksheet 7 Print Name: Signature: ID #: Instructor/Section: Directions: Show all your work for every problem. Problem Possible Points 1 10 2 10 3 10 4 10 5 10 6 15 7 10 8 15 9 10 Total 100 1
Background image of page 1

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

View Full Document Right Arrow Icon
2 (1) Find the derivative of the given function. (a) G ( x ) = 7 x 4 + 11 x + 1 (b) F ( x ) = ( x 2 - 1)( x - 3) (c) H ( x ) = (9 x 9 - 8 x 8 ) x + 1 x (d) J ( x ) = x 2 - 1 2 x + 3
Background image of page 2
3 (2) Find f 0 (0) given that h (0) = 3 and h 0 (0) = 2. (a) f ( x ) = xh ( x ) (b) f ( x ) = 3 x 2 h ( x ) - 5 x (c) f ( x ) = h ( x ) - 1 h ( x ) (d) f ( x ) = h ( x ) + x h ( x )
Background image of page 3

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

View Full Document Right Arrow Icon
4 (3) Find an equation for the tangent line to the graph of f ( x ) at the point ( a, f ( a )) (a) f ( x ) = x x + 2 ; a = - 4 (b) f ( x ) = ( x 2 - 3)(5 x - x 3 ); a = 1
Background image of page 4
5 (4) Find the points where the tangent line to the graph of f ( x ) is horizontal. (a) f ( x ) = ( x - 2)( x 2 - x - 11) (b) f ( x ) = 5 x x 2 + 1
Background image of page 5

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

View Full Document Right Arrow Icon
6 (5) (a) Verify that, if, f , g , h are differentiable, then ( fgh ) 0 ( x ) = f 0 ( x ) g ( x ) h ( x ) + f ( x ) g 0 ( x ) h ( x ) + f ( x ) g ( x ) h 0 ( x ) ( Hint: Apply the product rule to [ f ( x ) g ( x )] h ( x ) ) (b) Use the product rule to show that, if f is differentiable, then g ( x ) = [ f ( x )] 2 has derivative g 0 ( x ) = 2 f ( x ) f 0 ( x )
Background image of page 6
7 (6) Differentiate the given function:
Background image of page 7

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

View Full Document Right Arrow Icon
Background image of page 8
Background image of page 9

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

View Full Document Right Arrow Icon
Background image of page 10
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: (a) f ( x ) = (1-2 x )-1 (b) f ( x ) = ( x-x 3-x 5 ) 4 (c) f ( x ) = [(2 x + 1) 2 + ( x + 1) 2 ] 3 (d) f ( x ) = ± 4 x + 3 5 x-2 ² 3 8 (7) Given that f (0) = 1 , f (0) = 2 , f (1) = 0 , f (1) = 1 , f (2) = 1 , f (2) = 1 and g (0) = 2 , g (0) = 1 , g (1) = 1 , g (1) = 0 , g (2) = 2 , f (2) = 1 evaluate the following. (a) ( f ◦ g ) (0) = (b) ( g ◦ f ) (0) = (c) ( f ◦ g ) (1) = (d) ( g ◦ f ) (2) = 9 (8) Find the indicated derivative in terms of f ( x ) (a) d dx [ f ( x 2 + 1)] = (b) d dx ± f ( x )-1 f ( x ) + 1 ² = 10 (9) Determine the values of x for which f ( x ) = 0 and f ( x ) > 0. (a) f ( x ) = (1 + x 2 )-2 (b) f ( x ) = x (1-x 2 ) 3...
View Full Document

{[ snackBarMessage ]}