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Find the equation of the normals to the curve `y=x^3+2x+6`which are parallel to the line `x + 14 y + 4 = 0`.

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To find the equation of the normals to the curve \( y = x^3 + 2x + 6 \) that are parallel to the line \( x + 14y + 4 = 0 \), we can follow these steps: ### Step 1: Find the slope of the given line The equation of the line can be rewritten in slope-intercept form \( y = mx + b \). Starting with: \[ x + 14y + 4 = 0 ...
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NAGEEN PRAKASHAN ENGLISH-APPLICATIONS OF DERIVATIVES-Exercise 6.3
  1. Find a point on the curve y=(x-2)^2at which the tangent is parallel t...

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  2. Find the point on the curve y=x^3-11 x+5 at which the tangent is y"...

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  3. Find the equation of all lines having slope - 1that are tangents to th...

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  4. Find the equations of all lines having slope 2 and that are tangent...

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  5. Find the equations of all lines having slope 0 which are tangent to t...

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  6. Find pints on the curve (x^2)/9+(y^2)/(16)=1 at which the tangents ...

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  7. Find the equations of the tangent and normal to the given curves at ...

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  8. Find the equation of the tangent line to the curve y=x^2-2x+7which is(...

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  9. Show that the tangents to the curve y=7x^3+11at the points where x = ...

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  10. Find the points on the curve y=x^3 at which the slope of the tangen...

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  11. For the curve y=4x^3-2x^5 find all points at which the tangent pass...

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  12. Find the points on the curve x^2+y^2-2x-3=0at which the tangents are ...

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  13. Find the equation of the normal at the point (a m^2, a m^3) for the ...

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  14. Find the equation of the normals to the curve y=x^3+2x+6which are par...

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  15. Find the equations of the tangent and normal to the parabola y^2=4a x...

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  16. Show that the curves x=y^2 and x y=k cut at right angles, if 8k^2=1...

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  17. Find the equations of the tangent and normal to the hyperbola (x^2)/(...

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  18. Find the equation of the tangent to the curve y=sqrt(3x-2)which is par...

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  19. The slope of the normal to the curve y=2x^2+3sin x at x = 0is(A) 3 (B...

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  20. The line y = x + 1is a tangent to the curve y^2=4xat the point(A) (1...

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