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Find the slope of the tangent to curve y...

Find the slope of the tangent to curve `y=x^3-x+1` at the point whose x-coordinate is 2.

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To find the slope of the tangent to the curve \( y = x^3 - x + 1 \) at the point where the x-coordinate is 2, we will follow these steps: ### Step 1: Differentiate the function We start by differentiating the function \( y = x^3 - x + 1 \) with respect to \( x \). \[ \frac{dy}{dx} = \frac{d}{dx}(x^3) - \frac{d}{dx}(x) + \frac{d}{dx}(1) \] ...
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NAGEEN PRAKASHAN ENGLISH-APPLICATIONS OF DERIVATIVES-Exercise 6.3
  1. Find the slope of the tangent to the curve y = x^3- x at x = 2.

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

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  3. Find the slope of the tangent to curve y=x^3-x+1 at the point whose x...

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

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  5. Find the slope of the normal to the curve x=a\ cos^3theta , y=a\ sin...

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

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

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  8. Find a point on the curve y=(x-2)^2at which the tangent is parallel t...

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

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

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

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

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

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

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

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

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

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

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

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

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