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Application Of Derivatives

Question
CBSEENMA12035208
Wired Faculty App

Find point on the curve y = 3x2 – 12x + 6 at which tangent is parallel to x-axis. Also find the equation of tangent line. 

Solution

The equation of curve is
                  y = 3x2 – 12x + 6                                     ...(1)
therefore space space space space space space dy over dx space equals space 6 straight x minus 12 because space space space space space tangent space is space parallel space to space straight x minus axis therefore space space space space space space dy over dx space equals space 0 space space space space space space space space space space space space space space rightwards double arrow space space space space 6 straight x minus 12 space equals space 0 space space space space rightwards double arrow space space space straight x space equals space 2 Putting space space straight x space equals space 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 straight y equals 12 minus 24 plus 6 space equals space minus 6 therefore space space space space space space point space is space left parenthesis 2 comma space minus 6 right parenthesis The space equation space of space tangent space line space is space straight y space equals space minus 6         

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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