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Application Of Derivatives

Question
CBSEENMA12035210
Wired Faculty App

Find out on the curve y = 2 x2 – 6x – 4 at which tangent is parallel to x-axis. Also find the equation of tangent line.

Solution

The equation of curve is
                   y = 2x2 – 6x – 4                                ...(1)
therefore space space space space space space space space dy over dx space equals space 4 straight x minus 6
because space space space space tangent space is space parallel space to space straight x minus axis.
therefore space space space dy over dx space equals space 0 space space space space rightwards double arrow space space space space space 4 straight x minus 6 space equals space 0 space space space rightwards double arrow space space space space straight x space equals space 3 over 2 Putting space straight x space equals space 3 over 2 space in space left parenthesis 1 right parenthesis comma space we space get comma 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 space space space space space straight y space equals space 2 cross times 9 over 4 minus 6 cross times 3 over 2 minus 4 space space equals space 9 over 2 minus 9 minus 4 space equals space minus 17 over 2 The space equation space of space tangent space line space is space space space space space space space space space space space straight y space equals space minus 17 over 2 space space space space space or space space space space space space 2 straight y space equals space minus 17 space space space space or space space space 2 straight y plus 17 space equals space 0

 

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