Question

Find the equations of the tangent and normal to the curve y = x² + 4x + 1 at the point whose abscissa is 3.

Solution

The equation of curve is y = x² + 4x + 1 ...(1)
When x = 3, y = 9 + 12 + 1 = 22
$therefore$ point with abscissa 3 is (3, 22)
Diff. (1) w.r.t.x, $dy over dx space equals space 2 straight x plus 4$
At (3, 22), $dy over dx space equals space 6 plus 4 space equals space 10$
$therefore space space space space space slope space of space tangent space space equals space 10 therefore space space space space space space equation space of space the space tangent space at space left parenthesis 3 comma space 22 right parenthesis space is space space space space space space space space space space space space space space space space space space straight y space minus 22 space equals space 10 left parenthesis straight x minus 3 right parenthesis or space space space space space space space space space space space straight y minus 22 space equals space 10 straight x minus 30 space space space space or space space space 10 straight x minus straight y minus 8 space equals space 0 Also space slope space of space normal space space equals space minus 1 over 10 therefore space space space equation space of space normal space at space left parenthesis 3 comma space 222 right parenthesis space is space space space space space space straight y minus 22 space equals space minus 1 over 10 left parenthesis straight x minus 3 right parenthesis space space space space or space space space space space space 10 straight y minus 220 space equals space minus straight x plus 3 space space space or space space space straight x plus 10 straight y minus 223 space equals space 0$

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Application Of Derivatives

Find the equations of the tangent and normal to the curve y = x² + 4x + 1 at the point whose abscissa is 3.

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 equations of the tangent and normal to the curve y = x2 + 4x + 1 at the point whose abscissa is 3.

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 equations of the tangent and normal to the curve y = x² + 4x + 1 at the point whose abscissa is 3.