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Let I be any interval disjoint from [-1,...

Let I be any interval disjoint from `[-1,1]` Prove that the function f given by `f(x) = x + 1/x` is increasing on I.

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PSEB-APPLICATION OF DERIVATIVES-Exercise
  1. On which of the following intervals is the function f given by f(x) = ...

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  2. For what values of a the function f given by f(x) = x^2 +ax + 1 is inc...

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  3. Let I be any interval disjoint from [-1,1] Prove that the function f g...

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  4. Prove that the function f given by f(x) = log sinx, is increasing on (...

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  5. Prove that the function f given by f(x) = log |cosx| is decreasing on ...

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  6. Prove that the function given by f(x) = x^3 - 3x^2 + 3x - 100 is incre...

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  7. The interval in which y = x^2 e^-x is increasing is:

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  8. Find the slope of the tangent to the curve y = 3x^4-4x at x= 4

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

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

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

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

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  13. Find the slope of the normal to the curve x = 1 - a sin theta, y = b c...

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  14. Find points at which the tangent to the curve y = x^3-3x^2-9x+7 is par...

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  15. Find a point on the curve y = (x - 2)^2 at which the tangent is parall...

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

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  17. Find the equation of all lines having slope – 1 that are tangents to t...

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  18. Find the equations of all lines having slope 0 which are tangent to th...

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  19. Find points on the curve x^2/9+y^2/16 = 1 at which the tangents are pa...

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  20. Find points on the curve x^2/9+y^2/16 = 1 at which the tangents are pa...

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