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Let f(x) =e^(2x) -ae^(x)+1.Prove that f(...

Let `f(x) =e^(2x) -ae^(x)+1.`Prove that `f(x)` cannot be monotonically decreasing for `AA x in R` for any value of `a`

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RESONANCE ENGLISH-APPLICATION OF DERIVATIVES-Self Practice Problems
  1. Let f(x) =x - tan^(-1)x. Prove that f(x) is monotonically increasing ...

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  2. Find the range of values of a if f(x)=2e^x-a e^(-x)+(2a+1)x-3 is monot...

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  3. Let f(x) =e^(2x) -ae^(x)+1.Prove that f(x) cannot be monotonically d...

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  4. Find the values of a for which the function f(x)=(a+2)x^3-3a x^2+9a x-...

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  5. For each of the following graph comment on monotonically of f(x) ...

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  6. Let f(x)=x^3-3x^2+ 3x + 4, comment on the monotonic behaviour of f(x) ...

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  7. Draw the graph of function f(x)={underset([x] " "1 le x le 2)(x " ...

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  8. In each of following graphs identify if x= a is point of local maxi...

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  9. Examine the graph of following functions in each case identify the p...

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  10. Find the points of local maxima or minima of following functions...

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  11. Let f(x) =x^(3) -x^(2) -x-4 (i) find the possible points of maxim...

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  12. Let f(x) =x +(1)/(x). find local maximum and local minimum value ...

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  13. if f(x) ={underset( cos x " "x ge 0)((x+lambda)^(2) " " x lt 0). ...

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  14. Let f(x) = sin x (1+cos x) , x in (0,2pi). Find the number of criti...

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  15. Find the two positive numbers x and y whose sum is 35 and the ...

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  16. A square piece of tin of side 18 cm is to be made into a box withou...

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  17. A square piece of tin of side 18 cm is to be made into a box w...

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  18. The maximum distance of the centre of the ellipse x^2/(81)+y^2/(25)=1 ...

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  19. A line is drawn passing through point P(1,2) to cut positive coord...

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  20. Two towns A and B are situated on the same side of a straight road at ...

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