Question

Find the equation of the tangent and normal to the given curves at the points given:
y = x³ at (1, 1)

Solution

The equation of curve is y = x^{3
$therefore space space space space space dy over dx space equals space 3 straight x squared$}At (1, 1), $dy over dx space equals space 3 left parenthesis 1 right parenthesis squared space equals space 3$
$therefore space space space space straight m space equals space 3 comma space space where space straight m space is space slope space of space tangent. therefore space space space space space the space equation space of space tangent space at space left parenthesis 1 comma space 1 right parenthesis space is space space space space space space space space space space straight y minus 1 space equals space 3 left parenthesis straight x minus 1 right parenthesis semicolon space space space space space space or space space space straight y minus 1 space equals space 3 straight x minus 3 space space space space or space space space 3 straight x minus straight y minus 2 space equals space 0 Slope space of space normal space space equals space 1 third therefore space space space space equation space of space normal space at space left parenthesis 1 comma space 1 right parenthesis space is space space space space space space space space space space space space space space straight y minus 1 space equals space minus 1 third left parenthesis straight x minus 1 right parenthesis comma space space space space or space space space 3 straight y minus 3 space equals space minus straight x plus 1 space space space space or space space straight x plus 3 straight y minus 4 space equals space 0$

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Application Of Derivatives

Find the equation of the tangent and normal to the given curves at the points given:
y = x³ at (1, 1)

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.

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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 = x3 at (1, 1)

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 = x³ at (1, 1)