Prove that the tangents to the curve Y = x² – 5x + 6 at the points (2, 0) and (3, 0) are at right angles.

Solution

The equation of the curve is
y = x²– 5x + 6
$therefore space space space space dy over dx space equals 2 straight x minus 5$
Let $straight m subscript 1 comma space space straight m subscript 2$ be slopes of tangents to the curve at the points (2, 0), (3, 0).
$therefore space space space space straight m subscript 1 equals space space value space of space dy over dx space at space left parenthesis 2 comma space 0 right parenthesis space equals 2 left parenthesis 2 right parenthesis minus 5 space equals 4 minus 5 space equals space minus 1 space space space space space space space space straight m subscript 2 space equals space value space of space dy over dx space at space left parenthesis 3 comma space 0 right parenthesis space equals space 2 left parenthesis 3 right parenthesis space minus space 5 space equals space 6 minus 5 space equals space 1 therefore space space space straight m subscript 1 straight m subscript 2 space equals space left parenthesis negative 1 right parenthesis thin space left parenthesis 1 right parenthesis space equals space minus 1 therefore space tangents space to space the space given space curve space at space left parenthesis 2 comma space 0 right parenthesis comma space left parenthesis 3 comma space 0 right parenthesis space are space perpendicular space to space each space other.$

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Application Of Derivatives

Prove that the tangents to the curve Y = x² – 5x + 6 at the points (2, 0) and (3, 0) are at right angles.

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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NCERT Sample Papers

Entrance Exams Preparation

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For Daily Free Study Material Join wiredfaculty

Application Of Derivatives

Prove that the tangents to the curve Y = x2 – 5x + 6 at the points (2, 0) and (3, 0) are at right angles.

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

Prove that the tangents to the curve Y = x² – 5x + 6 at the points (2, 0) and (3, 0) are at right angles.