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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