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Application Of Derivatives

Question
CBSEENMA12035149
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Find the point on the curve y = x3 – 11 x + 5 at which the tangent has the equation y = x – 11.

Solution

The equation of the curve is y = x3 – 11 x + 5                               ...(1)
   therefore space space space space space dy over dx space equals space 3 straight x squared minus 11 comma space space space space which space is space slope space of space the space tangent space to space the space curve space left parenthesis 1 right parenthesis space at space left parenthesis straight x comma space straight y right parenthesis Consider space the space line space space straight y equals straight x minus 11 Its space slope space space equals space 1 therefore space space space space space 3 straight x squared minus 11 space equals space 1 space space space space rightwards double arrow space space space space 3 straight x squared space equals space 12 space space space space rightwards double arrow space space space space space straight x squared space equals space 4 space space space space space space rightwards double arrow space space space straight x space equals space 2 comma space space minus 2 When space straight x space equals space 2 comma space space from space left parenthesis 1 right parenthesis comma space space space space straight y space equals space 8 minus 22 plus 5 space equals space minus 9 When space straight x space equals space minus 2 comma space space from space left parenthesis 1 right parenthesis comma space space straight y space equals space minus 8 plus 22 plus 5 space equals space 19 therefore space space space space points space are space left parenthesis 2 comma space minus 9 right parenthesis space and space left parenthesis negative 2 comma space 19 right parenthesis comma space But space left parenthesis negative 2 comma space 19 right parenthesis space does space not space satisfy space the space line space straight y space equals space straight x minus 11 space space space space space as space space 19 space equals negative 2 minus 11 space is space not space true. space space space space space therefore space space space required space point space is space left parenthesis 2 comma space minus 9 right parenthesis.

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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