Compose the equation of the tangent and the equation of the normal to the graph of the function y=x^(2)-5x+4 if the abscissa of the tangent point x_(0)=-1

Truscelli3h 2022-09-14 Answered
Compose the equation of the tangent and the equation of the normal to the graph of the function y = x 2 5 x + 4 if the abscissa of the tangent point x 0 = 1
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Answers (1)

Francis Blanchard
Answered 2022-09-15 Author has 12 answers
y = x 2 5 x + 4
x 0 = 1 , y 0 = y ( x 0 ) = y ( 1 ) = ( 1 ) 2 5 ( 1 ) + 4 = 1 + 5 + 4 = 10
y = ( x 2 5 x + 4 ) = 2 x 2 1 5 + 0 = 2 x 1 5 = 2 x 5
y ( x 0 ) = y ( 1 ) = 2 ( 1 ) 5 = 2 5 = 7
tangent equations:
y y 0 = y ( x 0 ) ( x x 0 )
y 10 = 7 ( x ( 1 ) )
y 10 = 7 ( x + 1 )
y 10 = 7 x 7
7 x + y 3 = 0
normal equations:
y y 0 = 1 y ( x 0 ) ( x x 0 )
y 10 = 1 7 ( x ( 1 ) )
y 10 = 1 7 ( x + 1 )
7 y 70 = x + 1
x 7 y + 71 = 0
Answer: tangent 7 x + y 3 = 0, normal x 7 y + 71 = 0

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