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Without using the derivative, show that the function `f(x)=|x|` is strictly increasing in `(0,oo)` strictly decreasing in `(-oo,0)dot`

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RD SHARMA ENGLISH-INCREASING AND DECREASING FUNCTION -All Questions
  1. Prove that the function f given by f(x)=x-[x] us increasing in (0,1)do...

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

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  3. Without using the derivative, show that the function f(x)=|x| is stric...

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  4. Without using the derivative show that the function f(x)=7x-3 is stric...

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  5. Prove that the function f(x)=(log)a x is increasing on (0,oo) if a &...

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  6. Prove that f(x)=a x+b , where a , b are constants and a >0 is an incre...

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  7. Prove that the function f(x)=(log)e x is increasing on (0,oo)dot

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  8. Show that f(x)=1/(1+x^2) decreases in the interval [0,oo) and increase...

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  9. Show that f(x)=1/x is decreasing function on (0,oo)dot

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  10. Sol v e :(1-x^2)/(5x-6-x^2)<0

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  11. sol v e :1/(x+1)-4/((2+x)^2)>0,x!=-1,-2

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  12. Find dy/dx if x^2=siny

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  13. Find the intervals in which the function f(x)=2x^3+9x^2+12 x+20 is (i)...

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  14. Find the intervals in which f(x)=-x^2-2x+15 is increasing or decreasin...

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  15. Sol v e :(x^2-4x+7)/(x^2-7x+12)lt=2/3dot

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  16. Sol v e(8x^2+16 x-51)/(2x^2+5x-12)>3

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  17. Determine the values of x for which f(x)=x^x , x >0 is increasing or d...

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  18. Show that f(x) = 2x + cot^-1 x + log(sqrt(1+x^2)-x) is increasing in R

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  19. Find the intervals in which the function f(x)=x^4-(x^3)/3 is increasin...

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  20. Find the intervals in which f(x)=x/(logx) is increasing or decreasing.

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