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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 strictly increasing on I.

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A N EXCEL PUBLICATION-APPLICATION OF DERIVATIVES-QUESTION BANK
  1. On which of the following intervals is the function f given by f(x)=x^...

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  2. Find the least value of a such that the function f given by f(x)=x^2+a...

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

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  4. Prove that the function f given by f(x)=logsinx is strictly increasing...

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  5. Prove that the function f given by f(x)=logcosx is strictly decreasin...

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

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  7. The interval in which y=x^2e^(-x) is increasing is a) (0,2) b) (-2,0) ...

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  8. Find the equation of the tangent and normal at the point (1,2) on the ...

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  9. Find the point at which the tangent to the curve y=sqrt(4x-3)-1 has ...

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  10. Find the equation of all lines having slope 2 and being tangent to the...

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  11. Find points on the curve x^2/4+y^2/25=1 at which the tangents are para...

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  12. Find points on the curve x^2/4+y^2/25=1 at which the tangents are par...

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  13. Find the equation of tangent to the curve given by x=asin^3t,y=bcos^3t...

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

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  15. Find the slope of the tangent to the curve. y=(x-1)/(x-2),xne2 at x=...

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

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

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  18. Find the slope of the normal to the curve x=acos^3theta,y=asin^3theta"...

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  19. Find the slope of the normal to the curve x=1-asintheta ,y=bcos^2theta...

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

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