www.covenantuniversity.edu.ng Raising a new Generation of Leaders MAT121 DIFFERENTIATION {Application I} Dr. S.O. Edeki Application of Differentiation (I) . Equations of TANGENT and NORMAL to a curve y f ( x) will be considered. Recall: Two lines L1 and L 2 with gradients m1 and m2 respectively are said to be: (a) parallel if m1 m2 (b) perpendicular if m1m2 1 S.O. Edeki 2 Equation of TANGENT to a curve . (a) Equation of TANGENT to a curve y f ( x) at x x0 is: y y0 f ( x) x x0 NOTE: Use x x0 to obtain y0 via y f ( x) S.O. Edeki 3 Equation of NORMAL to a curve . (b) Equation of NORMAL to a curve y f ( x) at x x0 is: y y0 1 , f ( x) 0 x x0 f ( x) NOTE: Use x x0 to obtain y0 via y f ( x) S.O. Edeki 4 Ex1: TANGENT & NORMAL to a curve . (*) Find the equations of (a) tangent (T) and (b) normal (N) to the curve: (i) y x 3 x +x 1 at x 3 (ii) 1 y x at x 2 x 3 2 S.O. Edeki 5 Ex2: TANGENT & NORMAL to a curve . (*) Find the equations of (a) tangent (T) and (b) normal (N) to the curve: (i) y x 3x 1 at x 0 & x 4 (ii) y 2 x 5 x 4 at x 1 & x 1 2 3 S.O. Edeki 6