Posted on

MEI C2 Study Resources Core2 Differentiation 1-2 by Roger Porkess

By Roger Porkess

Show description

Read or Download MEI C2 Study Resources Core2 Differentiation 1-2 PDF

Similar nonfiction_4 books

Biomechanical Systems Technology: Muscular Skeletal Systems

Due to fast advancements in laptop expertise and computational options, advances in a large spectrum of applied sciences, coupled with cross-disciplinary targets among know-how and its program to human physique techniques, the sphere of biomechanics keeps to adapt. Many parts of important growth contain dynamics of musculoskeletal platforms, mechanics of demanding and smooth tissues, mechanics of bone home improvement, mechanics of blood and ventilation, flow-prosthesis interfaces, mechanics of influence, dynamics of man-machine interplay, and extra.

Progress in Understanding of Polymer Crystallization

Within the context of polymer crystallization there are numerous nonetheless open and infrequently controversially debated questions. the current quantity addresses concerns similar to novel normal perspectives and ideas which support to boost our knowing of polymer crystallisationnucleation phenomenalong residing soften constructions affecting crystallizationconfinement results on crystallizationcrystallization in flowing meltsfluid mobility regulations as a result of crystallitesthe position of mesophases within the crystal formationand provides new principles in a attached and obtainable means.

Everything You Ever Needed to Know about Training: A One-Stop Shop for Everyone Interested in Training, Learning and Development, 4th Edition

The function of coach has advanced in recent times to incorporate inner advisor, studying adviser, facilitator of studying, e-learning dressmaker and office trainer, and hence there's now a necessity for pro running shoes as a way to establish their contribution to organizational functionality. Now in its fourth version, every thing You Ever had to learn about education highlights the most phases of deciding on, designing, and providing studying and improvement courses.

Additional resources for MEI C2 Study Resources Core2 Differentiation 1-2

Example text

I) 24 x x 24 - 2x x 15 - 2x 15 x Height of box is x cm Length of box is (24 – 2x) cm Width of box is (15 – 2x) cm Volume V = x(15 − 2 x )(24 − 2 x ) = x(360 − 78 x + 4 x 2 ) = 4 x 3 − 78 x 2 + 360 x dV = 12 x 2 − 156 x + 360 dx At turning points, 12 x 2 − 156 x + 360 = 0 (ii) x 2 − 13 x + 30 = 0 ( x − 3)( x − 10) = 0 x = 3 or x = 10 © MEI, 11/08/08 6/7 MEI C2 Differentiation Section 2 Exercise solutions x = 10 is not possible since this would mean that the width would be negative. d2V = 24 x − 156 dx 2 d2V When x = 3, = 72 − 156 < 0 , so x = 1 is a maximum point.

Find the co-ordinates of any turning points and determine their nature showing clearly how your decisions were made. Sketch the curve. 4. The equation of a curve is y = (x +1)(x – 3)3. (i) Write the equation of the curve in the form y = ax4 + bx3 + cx2 + dx + e. dy (ii) Find the co-ordinates of the points where = 0. dx (iii) Classify the stationary points. (iv) Sketch the curve. 5. Find the stationary points on the curve y = x4 – 2x3 and distinguish between them, showing all of the relevant working clearly.

Iv) y = x 3 + 6 x 2 + 9 x = x( x 2 + 6 x + 9) = x( x + 3)2 The graph cuts the x-axis at x = 0 and x = -3 (repeated). The graph cuts the y-axis at y = 0. -3 (-1, -4) © MEI, 11/08/08 1/7 MEI C2 Differentiation Section 2 Exercise solutions 2. (i) y = 2 x + x 2 − 4 x 3 dy dx = 2 + 2 x − 12 x 2 dy =0 dx 2 + 2 x − 12 x 2 = 0 At turning points, 1 + x − 6x 2 = 0 6x 2 − x − 1 = 0 (3 x + 1)(2 x − 1) = 0 x = − 31 or x = 21 2 3 4 = When x = − 31 , y = 2 ( − 31 ) + ( − 31 ) − 4 ( − 31 ) = − 23 + 19 + 27 When x = 21 , y = 2 ( 21 ) + ( 21 ) − 4 ( 21 ) = 1 + 41 − 21 = 2 3 11 The turning points are ( − 31 , − 27 ) and x< − 31 -ve x dy x = − 31 0 −18 + 3 + 4 27 11 = − 27 3 4 ( 21 , 43 ) .

Download PDF sample

Rated 4.26 of 5 – based on 29 votes