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  • I have a doubt, kindly clarify. - Limit , continuity and differentiability - JEE Main-14

Let ax+ by + 1 = 0 is equation of tangent to y = x^3 + x - 1  at (2, 9) then 17(a + b) equals

  • Option 1)

    -11

  • Option 2)

    -12

  • Option 3)

    -13

  • Option 4)

    -14

 

Answers (1)

best_answer

As we have learned

Condition for a given line to touch the given curve -

Let the line be a tangent to the given curve at (x1, y1) then write the equation of the tangent as 

(y-y_{1})=\frac{dy}{dx}(x-x_{1})

Comparing the equation with the given equation 

ax+by+c= 0

-

 

 \frac{dy}{dx}= 3x^{2}+1\Rightarrow \frac{dy}{dx} .. at..(2,9) = 3(2)^{2}+1=13

\therefore Equation of tangent : -- 

y-9=13(x-2)

\Rightarrow y= 13x-17\Rightarrow -13x+y +17=0

\Rightarrow \frac{-13}{17}x+\frac{1}{17}y+1=0

a= -13/17.. and .. b= 1/17

\Rightarrow a+b = -12/17\Rightarrow 17(a+b) = -12

 

 

 

 

 


Option 1)

-11

Option 2)

-12

Option 3)

-13

Option 4)

-14

Posted by

Himanshu

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