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Show that for any real numbers lambda, t...

Show that for any real numbers `lambda`, the polynomial `P(x)=x^7+x^3+lambda`, has exactly one real root.

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RESONANCE ENGLISH-APPLICATION OF DERIVATIVES-Self Practice Problems
  1. Let f(x)=x^3-3x^2+ 3x + 4, comment on the monotonic behaviour of f(x) ...

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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  16. Prove the following inequality: e^(x) gt x+1 " "" for"" " x in (...

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  17. if f (x) satisfies condition in Rolle's theorem then show that betw...

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  18. Show that for any real numbers lambda, the polynomial P(x)=x^7+x^3+lam...

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  19. Using LMVT, prove that if two functions have equal derivatives at all ...

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  20. if a function f(x) is (i) continuous on [a,b] (ii) derivable on (...

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