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Show that the function x^2-x+1 is neithe...

Show that the function `x^2-x+1` is neither increasing nor decreasing on `(0,\ 1)` .

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To show that the function \( f(x) = x^2 - x + 1 \) is neither increasing nor decreasing on the interval \( (0, 1) \), we will follow these steps: ### Step 1: Differentiate the function We start by finding the derivative of the function \( f(x) \). \[ f(x) = x^2 - x + 1 \] ...
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RD SHARMA-INCREASING AND DECREASING FUNCTION -Solved Examples And Exercises
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  2. Show that f(x)=(x-1)e^x+1 is an increasing function for all x >0 .

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  3. Show that the function x^2-x+1 is neither increasing nor decreasing...

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  4. Show that f(x)=x^9+4x^7+11 is an increasing function for all x in ...

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  5. Prove that the function f(x)=x^3-6x^2+12 x-18 is increasing on R .

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  6. State when a function f(x) is said to be increasing on an interval ...

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  7. Show that f(x)=sinx-cosx is an increasing function on (-pi//4,\ pi//4)...

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  8. Show that f(x)=tan^(-1)x-x is decreasing function on Rdot

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  9. Determine whether f(x)=-x/2+sinx is increasing or decreasing on (-pi/3...

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  10. Find the intervals in which f(x)=log(1+x)-x/(1+x) is increasing or dec...

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  11. Find the intervals in which f(x)=(x+2)e^(-x) is increasing or decreasi...

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  12. Show that the function f given by f(x)=10^x is increasing for all x .

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  13. Prove that the function f given by f(x)=x-[x] is increasing in (0,\ 1)...

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  14. Prove that the function f(x)=3x^5+40 x^3+240 x is increasing on R .

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  15. Prove that the function f given by f(x)=logcosx is strictly increasing...

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  16. Show that the function f given by f(x)=x^3-3x^2+4x ,x in Ris strictl...

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  17. Prove that the function f(x)=cosx is strictly decreasing in (0,\ pi)

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  18. Prove that the function f(x)=cosx is strictly increasing in (pi,\ 2pi)

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  19. Prove that the function f(x)=cosx is neither increasing nor decreas...

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  20. Show that f(x)=x^2-xsinx is an increasing function on (0,\ pi//2) .

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