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Show that the function f(x) = 2x+1 is st...

Show that the function f(x) = 2x+1 is strictly increasing on R.

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f(x) 2x+1
Let `x_(1), x_(2) in R and x_(1)ltx_(2)`
`"Now "x_(1)ltx_(2)`
`rArr 2x_(1)lt 2x_(2)`
`rArr 2x_(1)+1 lt 2x_(2) +1 `
`rArr f(x_(1))lt f (x_(2))`
`:. " "x_(1)lt x_(2)`
`rArr f(x_(1))lt f(x_(2))forall x_(1), x_(2) in R`
`rArr ` f(x) is strictly increasing on R.
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NAGEEN PRAKASHAN-APPLICATIONS OF DERIVATIVES-Miscellaneous Exercise
  1. Show that the function f(x) = 2x+1 is strictly increasing on R.

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  3. Show that the function given by f(x)=(logx)/xhas maximum at x = e.

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  4. The two equal sides of an isosceles triangle with fixed base b are ...

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  5. Find the equation of the normal to the curve x^2=4ywhich passes throu...

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  6. Show that the normal at any point theta to the curve x=acostheta+at...

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  7. Find the intervals in which the function f given by f(x)=(4sinx-2x-x c...

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  8. Find the intervals in which the function f given by f(x)=\ x^3+1/(...

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  9. Find the maximum area of an isosceles triangle inscribed in the ellip...

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  10. A tank with rectangular base and rectangular sides, open at the top is...

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  11. The sum of the perimeter of a circle and square is k, where k is so...

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  13. A point on the hypotenuse of a triangle is at distance a and b from t...

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  15. Find the absolute maximum and minimum values of the function f give...

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  16. Show that the altitude of the right circular cone of maximum volume...

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  17. Let f be a function defined on [a, b] such that f^(prime)(x)>0, for al...

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  18. Show that the height of the cylinder of maximum volume that can be in...

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  19. Show that height of the cylinder of greatest volume which can be insc...

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  20. A cylindrical tank of radius 10 m is being filled with wheat at the r...

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