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Application Of Derivatives

Question
CBSEENMA12035106
Wired Faculty App

Find the equation of the tangent and normal lines to the curve
straight y space equals sin squared straight x space at space space space straight x space equals space straight pi over 2.

Solution

The equation of curve is straight y space equals space sin squared straight x                                  ...(1)
therefore space space space space dy over dx space equals space 2 space sinx space cosx space space equals space sin space 2 straight x
At space space straight x space equals space straight pi over 2 comma space space space dy over dx space equals space sin space straight pi space equals space 0 therefore space space space space slope space of space tangent space space equals space 0 When space straight x space equals space straight pi over 2 comma space space space space space space space straight y space equals space sin squared straight pi over 2 space equals space 1 therefore space space space point space is space open parentheses straight pi over 2 comma space space 1 close parentheses The space equation space of space tangent space at space open parentheses straight pi over 2 comma space space 1 close parentheses space is space space space space space space space space space space space space space space space space space space space space space space space space space straight y space minus space 1 space equals space 0 space open parentheses straight x minus straight pi over 2 close parentheses space space space or space space space space straight y minus 1 space equals space 0
Since tangent is parallel to x-axis.
therefore space space space space space normal space is space parallel space to space straight y minus axis therefore space space space space space space equation space of space normal space through space open parentheses straight pi over 2 comma space space 1 close parentheses space is space space space space space space space space space space space space space straight x space equals space straight pi over 2 space space space space space or space space space space space straight x minus straight pi over 2 space equals space 0.

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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