11X1 T12 01 first derivative (2010)

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<ul><li><p>Geometrical Applications </p><p>of Differentiation The First Derivative </p></li><li><p>Geometrical Applications </p><p>of Differentiation The First Derivative </p><p>dx</p><p>dyxf</p><p>dx</p><p>dxfy ,,, </p></li><li><p>Geometrical Applications </p><p>of Differentiation The First Derivative </p><p>dx</p><p>dyxf</p><p>dx</p><p>dxfy ,,, </p><p>curve a o tangent t theof slope themeasures dx</p><p>dy</p></li><li><p>Geometrical Applications </p><p>of Differentiation The First Derivative </p><p>dx</p><p>dyxf</p><p>dx</p><p>dxfy ,,, </p><p>curve a o tangent t theof slope themeasures dx</p><p>dy</p><p> increasing is curve the,0 If xf</p></li><li><p>Geometrical Applications </p><p>of Differentiation The First Derivative </p><p>dx</p><p>dyxf</p><p>dx</p><p>dxfy ,,, </p><p>curve a o tangent t theof slope themeasures dx</p><p>dy</p><p> increasing is curve the,0 If xf</p><p> decreasing is curve the,0 If xf</p></li><li><p>Geometrical Applications </p><p>of Differentiation The First Derivative </p><p>dx</p><p>dyxf</p><p>dx</p><p>dxfy ,,, </p><p>curve a o tangent t theof slope themeasures dx</p><p>dy</p><p> increasing is curve the,0 If xf</p><p> decreasing is curve the,0 If xf</p><p> stationary is curve the,0 If xf</p></li><li><p>Geometrical Applications </p><p>of Differentiation The First Derivative </p><p>dx</p><p>dyxf</p><p>dx</p><p>dxfy ,,, </p><p>curve a o tangent t theof slope themeasures dx</p><p>dy</p><p> increasing is curve the,0 If xf</p><p>curve sketch the Hence </p><p>nature. their determine and </p><p>points stationary theof all find ,3 curve For the e.g. 32 xxy </p><p> decreasing is curve the,0 If xf</p><p> stationary is curve the,0 If xf</p></li><li><p>Geometrical Applications </p><p>of Differentiation The First Derivative </p><p>dx</p><p>dyxf</p><p>dx</p><p>dxfy ,,, </p><p>curve a o tangent t theof slope themeasures dx</p><p>dy</p><p> increasing is curve the,0 If xf</p><p>curve sketch the Hence </p><p>nature. their determine and </p><p>points stationary theof all find ,3 curve For the e.g. 32 xxy </p><p> decreasing is curve the,0 If xf</p><p> stationary is curve the,0 If xf</p><p>236 xxdx</p><p>dy</p></li><li><p>0 occur when points Stationary dx</p><p>dy</p></li><li><p>0 occur when points Stationary dx</p><p>dy</p><p>036 .. 2 xxei</p></li><li><p>0 occur when points Stationary dx</p><p>dy</p><p>036 .. 2 xxei</p><p>2or 0</p><p>023</p><p>xx</p><p>xx</p></li><li><p>0 occur when points Stationary dx</p><p>dy</p><p>036 .. 2 xxei</p><p>2or 0</p><p>023</p><p>xx</p><p>xx</p><p> 2,4 and 0,0at occur points stationary</p></li><li><p>0 occur when points Stationary dx</p><p>dy</p><p>036 .. 2 xxei</p><p>2or 0</p><p>023</p><p>xx</p><p>xx</p><p> 2,4 and 0,0at occur points stationary</p><p> 0,0</p></li><li><p>0 occur when points Stationary dx</p><p>dy</p><p>036 .. 2 xxei</p><p>2or 0</p><p>023</p><p>xx</p><p>xx</p><p> 2,4 and 0,0at occur points stationary</p><p> 0,0</p><p>x </p><p>dx</p><p>dy</p></li><li><p>0 occur when points Stationary dx</p><p>dy</p><p>036 .. 2 xxei</p><p>2or 0</p><p>023</p><p>xx</p><p>xx</p><p> 2,4 and 0,0at occur points stationary</p><p> 0,0</p><p>x </p><p>dx</p><p>dy</p><p>0 </p></li><li><p>0 occur when points Stationary dx</p><p>dy</p><p>036 .. 2 xxei</p><p>2or 0</p><p>023</p><p>xx</p><p>xx</p><p> 2,4 and 0,0at occur points stationary</p><p> 0,0</p><p>x </p><p>dx</p><p>dy</p><p>0 </p><p>0 </p></li><li><p>0 occur when points Stationary dx</p><p>dy</p><p>036 .. 2 xxei</p><p>2or 0</p><p>023</p><p>xx</p><p>xx</p><p> 2,4 and 0,0at occur points stationary</p><p> 0,0</p><p>x </p><p>dx</p><p>dy</p><p>0 </p><p>0 </p><p>0</p></li><li><p>0 occur when points Stationary dx</p><p>dy</p><p>036 .. 2 xxei</p><p>2or 0</p><p>023</p><p>xx</p><p>xx</p><p> 2,4 and 0,0at occur points stationary</p><p> 0,0</p><p>x </p><p>dx</p><p>dy</p><p>0 </p><p>0 </p><p>0 0</p></li><li><p>0 occur when points Stationary dx</p><p>dy</p><p>036 .. 2 xxei</p><p>2or 0</p><p>023</p><p>xx</p><p>xx</p><p> 2,4 and 0,0at occur points stationary</p><p> 0,0</p><p>x </p><p>dx</p><p>dy</p><p>0 </p><p>0 </p><p>0 0(-1) </p></li><li><p>0 occur when points Stationary dx</p><p>dy</p><p>036 .. 2 xxei</p><p>2or 0</p><p>023</p><p>xx</p><p>xx</p><p> 2,4 and 0,0at occur points stationary</p><p> 0,0</p><p>x </p><p>dx</p><p>dy</p><p>0 </p><p>0 </p><p>0 0(-1) </p><p>(-9) </p></li><li><p>0 occur when points Stationary dx</p><p>dy</p><p>036 .. 2 xxei</p><p>2or 0</p><p>023</p><p>xx</p><p>xx</p><p> 2,4 and 0,0at occur points stationary</p><p> 0,0</p><p>x </p><p>dx</p><p>dy</p><p>0 </p><p>0 </p><p>0 0(-1) (1) </p><p>(-9) </p></li><li><p>0 occur when points Stationary dx</p><p>dy</p><p>036 .. 2 xxei</p><p>2or 0</p><p>023</p><p>xx</p><p>xx</p><p> 2,4 and 0,0at occur points stationary</p><p> 0,0</p><p>x </p><p>dx</p><p>dy</p><p>0 </p><p>0 </p><p>0 0(-1) (1) </p><p>(-9) (3) </p></li><li><p>0 occur when points Stationary dx</p><p>dy</p><p>036 .. 2 xxei</p><p>2or 0</p><p>023</p><p>xx</p><p>xx</p><p> 2,4 and 0,0at occur points stationary</p><p> 0,0</p><p>x </p><p>dx</p><p>dy</p><p>0 </p><p>0 </p><p>0 0(-1) (1) </p><p>(-9) (3) </p><p> point turningminimum a is 0,0</p></li><li><p>0 occur when points Stationary dx</p><p>dy</p><p>036 .. 2 xxei</p><p>2or 0</p><p>023</p><p>xx</p><p>xx</p><p> 2,4 and 0,0at occur points stationary</p><p> 0,0</p><p>x </p><p>dx</p><p>dy</p><p>0 </p><p>0 </p><p>0 0(-1) (1) </p><p>(-9) (3) </p><p> point turningminimum a is 0,0</p><p> 2,4</p></li><li><p>0 occur when points Stationary dx</p><p>dy</p><p>036 .. 2 xxei</p><p>2or 0</p><p>023</p><p>xx</p><p>xx</p><p> 2,4 and 0,0at occur points stationary</p><p> 0,0</p><p>x </p><p>dx</p><p>dy</p><p>0 </p><p>0 </p><p>0 0(-1) (1) </p><p>(-9) (3) </p><p> point turningminimum a is 0,0</p><p> 2,4</p><p>x </p><p>dx</p><p>dy</p></li><li><p>0 occur when points Stationary dx</p><p>dy</p><p>036 .. 2 xxei</p><p>2or 0</p><p>023</p><p>xx</p><p>xx</p><p> 2,4 and 0,0at occur points stationary</p><p> 0,0</p><p>x </p><p>dx</p><p>dy</p><p>0 </p><p>0 </p><p>0 0(-1) (1) </p><p>(-9) (3) </p><p> point turningminimum a is 0,0</p><p> 2,4</p><p>x </p><p>dx</p><p>dy</p><p>2 </p></li><li><p>0 occur when points Stationary dx</p><p>dy</p><p>036 .. 2 xxei</p><p>2or 0</p><p>023</p><p>xx</p><p>xx</p><p> 2,4 and 0,0at occur points stationary</p><p> 0,0</p><p>x </p><p>dx</p><p>dy</p><p>0 </p><p>0 </p><p>0 0(-1) (1) </p><p>(-9) (3) </p><p> point turningminimum a is 0,0</p><p> 2,4</p><p>x </p><p>dx</p><p>dy</p><p>2 </p><p>0 </p></li><li><p>0 occur when points Stationary dx</p><p>dy</p><p>036 .. 2 xxei</p><p>2or 0</p><p>023</p><p>xx</p><p>xx</p><p> 2,4 and 0,0at occur points stationary</p><p> 0,0</p><p>x </p><p>dx</p><p>dy</p><p>0 </p><p>0 </p><p>0 0(-1) (1) </p><p>(-9) (3) </p><p> point turningminimum a is 0,0</p><p> 2,4</p><p>x </p><p>dx</p><p>dy</p><p>2 </p><p>0 </p><p>2</p></li><li><p>0 occur when points Stationary dx</p><p>dy</p><p>036 .. 2 xxei</p><p>2or 0</p><p>023</p><p>xx</p><p>xx</p><p> 2,4 and 0,0at occur points stationary</p><p> 0,0</p><p>x </p><p>dx</p><p>dy</p><p>0 </p><p>0 </p><p>0 0(-1) (1) </p><p>(-9) (3) </p><p> point turningminimum a is 0,0</p><p> 2,4</p><p>x </p><p>dx</p><p>dy</p><p>2 </p><p>0 </p><p>2 2</p></li><li><p>0 occur when points Stationary dx</p><p>dy</p><p>036 .. 2 xxei</p><p>2or 0</p><p>023</p><p>xx</p><p>xx</p><p> 2,4 and 0,0at occur points stationary</p><p> 0,0</p><p>x </p><p>dx</p><p>dy</p><p>0 </p><p>0 </p><p>0 0(-1) (1) </p><p>(-9) (3) </p><p> point turningminimum a is 0,0</p><p> 2,4</p><p>x </p><p>dx</p><p>dy</p><p>2 </p><p>0 </p><p>2 2(1) </p></li><li><p>0 occur when points Stationary dx</p><p>dy</p><p>036 .. 2 xxei</p><p>2or 0</p><p>023</p><p>xx</p><p>xx</p><p> 2,4 and 0,0at occur points stationary</p><p> 0,0</p><p>x </p><p>dx</p><p>dy</p><p>0 </p><p>0 </p><p>0 0(-1) (1) </p><p>(-9) (3) </p><p> point turningminimum a is 0,0</p><p> 2,4</p><p>x </p><p>dx</p><p>dy</p><p>2 </p><p>0 </p><p>2 2(1) </p><p>(3) </p></li><li><p>0 occur when points Stationary dx</p><p>dy</p><p>036 .. 2 xxei</p><p>2or 0</p><p>023</p><p>xx</p><p>xx</p><p> 2,4 and 0,0at occur points stationary</p><p> 0,0</p><p>x </p><p>dx</p><p>dy</p><p>0 </p><p>0 </p><p>0 0(-1) (1) </p><p>(-9) (3) </p><p> point turningminimum a is 0,0</p><p> 2,4</p><p>x </p><p>dx</p><p>dy</p><p>2 </p><p>0 </p><p>2 2(1) (3) </p><p>(3) </p></li><li><p>0 occur when points Stationary dx</p><p>dy</p><p>036 .. 2 xxei</p><p>2or 0</p><p>023</p><p>xx</p><p>xx</p><p> 2,4 and 0,0at occur points stationary</p><p> 0,0</p><p>x </p><p>dx</p><p>dy</p><p>0 </p><p>0 </p><p>0 0(-1) (1) </p><p>(-9) (3) </p><p> point turningminimum a is 0,0</p><p> 2,4</p><p>x </p><p>dx</p><p>dy</p><p>2 </p><p>0 </p><p>2 2(1) (3) </p><p>(3) (-9) </p></li><li><p>0 occur when points Stationary dx</p><p>dy</p><p>036 .. 2 xxei</p><p>2or 0</p><p>023</p><p>xx</p><p>xx</p><p> 2,4 and 0,0at occur points stationary</p><p> 0,0</p><p>x </p><p>dx</p><p>dy</p><p>0 </p><p>0 </p><p>0 0(-1) (1) </p><p>(-9) (3) </p><p> point turningminimum a is 0,0</p><p> 2,4</p><p>x </p><p>dx</p><p>dy</p><p>2 </p><p>0 </p><p>2 2(1) (3) </p><p>(3) (-9) </p><p> point turningmaximum a is 2,4</p></li><li><p>x </p><p>y </p></li><li><p>x </p><p>y </p></li><li><p>x </p><p>y </p><p> 2,4</p></li><li><p>x </p><p>y </p><p> 2,4</p><p>323 xxy </p></li><li><p>Exercise 10A; 1, 2ace, 4, 5, 6ac, 7, 8, 9ace etc, </p><p>11, 12, 13, 15ace, 16, 17 </p><p>Exercise 10B; 1ad, 2ac, 3ac, 5, 6, 7ac, 8, 10, 12 </p></li></ul>