Question

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Tentukan persamaan garis singgung pada kurva y = 2x^2 + x + 1 yang tegak lurus garis x + 5y - 4 = 0.

Answer 1

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gradien m1 , garis x+ 5y - 4 = 0
m1 = - 1/5
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kurva y = 2x² + x + 1
gradien garis singgung = m2
m2 = y' = 4x + 1
m2  = - 1/m1
m2 =  5

4x + 1 = 5
4x = 4
x = 1 , sub  kurva  y = 2x² + x + 1
y = 2+1+1 = 4
titiksinggung (x,y)= 1,4)

pers grs singgung y - y1 = m(x-x1)
y - 4 = 5(x - 1)
y = 5x - 5 + 4
y = 5x - 1
5x - y - 1= 0
..

Answer 2

X + 5y - 4 = 0
y= 4 - x / 5

y' = u' v - v' u / v^2
   = -1 (5) - 0 / 25
   = -1 /5 = m1

m1 . m2 = -1
-1/5 . m2 = -1
m2 = 5

y= 2x^2 + x + 1
y' = m2 = 4x + 1
       5 = 4x +1
       4 = 4x
       x = 1

masukkan x=1 ke y= 2x^2 +x +1
y= 2+ 1+ 1
  = 4
(x, y) = (1, 4)

y- y1 = m (x- x1)
y - 4 = 5 (x- 1)
y = 5x - 5 + 4
y= 5x - 1