Assignment-17-class-notes

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Queensland University of Technology **We aren't endorsed by this school
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BUSINESS MISC
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Mathematics
Date
Nov 2, 2023
Pages
5
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Studocu is not sponsored or endorsed by any college or university Assignment 17 - class notes Mathematics IA (The University of Adelaide) Studocu is not sponsored or endorsed by any college or university Assignment 17 - class notes Mathematics IA (The University of Adelaide) Downloaded by Alice Yu ([email protected]) lOMoARcPSD|32041740
Cambridge Senior Mathematcs for the Australian Curriculum/VCE Chapter 17 Diferentaton and antdiferentaton: Assignment 1 Consider a curve with equation y = 2 x 2 + x . a If P is the point (1, 3) and Q is the point ((1 + h ), 2(1 + h ) 2 + (1 + h )). Find the gradient of chord PQ . b Find the gradient of PQ when h = 0.1. c Find the gradient of the curve at P . 2 For the function f ( x ) = 2 x 2 , find . ) ( ) ( lim 0 h x f h x f h 3 Evaluate the following limits: a x x x 9 ) 3 ( lim 2 0 b h h h h h 2 3 0 2 lim c 2 8 lim 3 2 x x x 4 Find the derivative of each of the following: a 4 3 8 3 x x y b ) 2 ( 2 3 2 x x x y c ) 1 )( 3 2 ( x x y d ) ( 3 3 4 x x x x y e x x x x y 2 3 5 2 f x x x y 3 2 6 2 3 g 7 1 7 2 4 x x y h x x y 2 3 2 5 Let 8 2 3 4 x x x y . a Find the average rate of change of y between x = 1 and x = 2. b Find the gradient of the curve at x = 2. 6 For the graph shown, sketch the graph of the gradient function. 1 © Evans, Lipson, Wallace 2016 Downloaded by Alice Yu ([email protected]) lOMoARcPSD|32041740
Cambridge Senior Mathematcs for the Australian Curriculum/VCE Chapter 17 Diferentaton and antdiferentaton: Assignment 7 If 18 3 2 x x y find the interval(s) for which . 0 dx dy 8 The function 3 6 3 ) ( 2 3 t t t s represents the displacement of a particle moving along a straight line, where t is in seconds and s is in metres. a Find the position of the particle after 3 seconds. b Find the velocity of the particle at that time. 9 The curve with equation y = ax 2 + bx has a gradient of 5 at the point (1, -2). a Find the values of a and b . b Find the coordinates of the point where the gradient is 0. 10 For the graph of f : R R , find: a { x : f ′( x ) > 0} b { x : f ′( x ) < 0} c { x : f ′( x ) = 0} 11 Find the coordinates of the points on the curve y = x 2 + 5 x + 3 at which the tangent: a makes an angle of 45° with the positive direction of the x -axis b is parallel to the line y = 3 x + 4. 12 Consider the equation y = x ( x 2 - 9). a Find the gradient at the points at which the curve crosses the x -axis. b Find the coordinates of the point on the curve at which the gradient = 0. 2 © Evans, Lipson, Wallace 2016 Downloaded by Alice Yu ([email protected]) lOMoARcPSD|32041740
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