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The points at which the tangents to the curve `y=x^(3)-12x+18` are parallel to the X-axis are

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Tangent to the curve is parallel to the axis is when slope of the tangent is `0`
`:.` Equation of the curve is `y=x^3-3x^2-9x+7=0`..........(i)
`:. (dy)/(dx)=3x^2-6x-9`
Now, the tangent is parallel to x-axis. then slope of the tangent is zero or we can say that `(dy)/(dx)=0`
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NCERT ENGLISH-APPLICATION OF DERIVATIVES-EXERCISE 6.3
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  4. For the curve y=4x^3-2x^5, find all the points at which the tangents p...

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  5. Find the slope of the tangent to the curve y=(x-1)/(x-2), x!=2at x= 10...

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  6. The slope of the tangent to the curve y=x^(3) -x +1 at the point whose...

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  7. Find the slope of the tangent to the curve y=3x^4-4xat x = 4.

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  8. Find the slope of the normal to the curve x=1-asintheta , y=b\ cos^...

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  9. The points at which the tangents to the curve y=x^(3)-12x+18 are paral...

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  10. Find the slope of the tangent to the curve y=x^3-3x+2 at the point wh...

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  11. Find the slope of the normal to the curve x=acos^3theta,y=sin^3thetaat...

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  12. Find the point on the curve y = (x - 2)^(2) at which the tangent is pa...

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  13. Find the point on the curve y=x^3-11x +5 at which the equation of tang...

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

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

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

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

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

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

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