Question

Find the equation of the tangent and normal to the given curves at the points given:
y = x⁴ – 6x³ + 13x² – 10x + 5 at ( 0 , 5 )

Solution

The equations of curve is y = x⁴ – 6x³ + 13x² – 10x + 5
$therefore space space space space dy over dx space equals space 4 straight x cubed minus 3 bx squared plus 26 straight x minus 10$
At (0, 5). $dy over dx space equals space 0 minus 0 plus 0 minus 10 space equals space minus 10 comma space space which space is space slope space of space tangent$
$therefore space space space space space space equation space of space tangent space at thin space left parenthesis 0 comma space 5 right parenthesis space is space space space space space space space straight y space minus space 5 space space equals space minus 10 left parenthesis straight x minus 0 right parenthesis comma space space space space or space space space space straight y minus 5 space equals space minus 10 space straight x space space space space space or space space space 10 straight x plus straight y minus 5 space equals space 0 Slope space of space normal space equals space 1 over 10 therefore space space space space space space space equation space of space normal space at space left parenthesis 0 comma space 5 right parenthesis space is space space space space space space space space space space straight y minus 5 space equals space 1 over 10 left parenthesis straight x minus 0 right parenthesis or space space space space 10 straight y minus 50 space equals space straight x space space space space space space or space space space straight x minus 10 straight y plus 50 space equals space 0$

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Application Of Derivatives

Find the equation of the tangent and normal to the given curves at the points given:
y = x⁴ – 6x³ + 13x² – 10x + 5 at ( 0 , 5 )

Some More Questions From Application of Derivatives Chapter

The radius of a circle is increasing uniformly at the rate of 4 cm per second Find the rate at which the area of the circle is increasing when the radius is 8 cm.

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation

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For Daily Free Study Material Join wiredfaculty

Application Of Derivatives

Find the equation of the tangent and normal to the given curves at the points given:y = x4 – 6x3 + 13x2 – 10x + 5 at ( 0 , 5 )

Some More Questions From Application of Derivatives Chapter

The radius of a circle is increasing uniformly at the rate of 4 cm per second Find the rate at which the area of the circle is increasing when the radius is 8 cm.

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation

Find the equation of the tangent and normal to the given curves at the points given:
y = x⁴ – 6x³ + 13x² – 10x + 5 at ( 0 , 5 )