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Find the points on the curve y=x^3-2x^2+...

Find the points on the curve `y=x^3-2x^2+x` at which the tangents are parallel to x-axis. Also find the tangents at these points.

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  9. Find the acute angle between the two curves y=x^2 and y=(x-3)^2

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  10. Find (d^2y)/(dx^2) if y=2x^3-3x^2+5x-7

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  11. Find (d^2y)/(dx^2) if y=(x-1)/(x+1)

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  12. Find (d^2y)/(dx^2) if y=log(x+sqrt(x^2+a^2))

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  13. Find (d^2y)/(dx^2) if y=sin^3x.cosx

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  14. Find (d^2y)/(dx^2) if y=tan^(-1)2x

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  15. Find (d^2y)/(dx^2) if y=e^x.tanx

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  16. Find (d^2y)/(dx^2) at x=2 if y=x^3+logx

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  18. If y=(sin^(-1)x)^2, then prove that (1-x^2)y2-xy1=2

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  19. If y=(tan^(-1)x)^2 , show that (x^2+1)^2y2+2x(x^2+1)y1=2 .

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  20. If y=ae^(3x), then prove that (d^2y)/(dx^2)=9y.

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