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Show that f(x)=(x-1)e^x+1 is an increasi...

Show that `f(x)=(x-1)e^x+1` is an increasing function for all `x > 0.`

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`f(x)=(x-1) e^{x}+1 `
` f^{prime}(x)=(x-1) e^{x}+e^{x} `
` =x e^{x}-e^{x}+e^{x} `
` =x e^{x} `
Given :` x>0 `
We know
`e^{x}>0 `
` Rightarrow x e^{x}>0 `
` ...
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RD SHARMA-INCREASING AND DECREASING FUNCTION -Solved Examples And Exercises
  1. Show that f(x)=(x-1)e^x+1 is an increasing function for all x > 0.

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  2. Find the intervals in which f(x) is increasing or decreasing: (1). f(...

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  3. Show that f(x)=x^3-15 x^2+75 x-50 is an increasing function for all x...

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  4. Show that f(x)=cos^2x is decreasing function on (0,pi/2)dot

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

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  6. Show that f(x)=cosx is decreasing function on (0,pi), increasing in (-...

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  7. Show that f(x)=tan^(-1)(sinx+cosx) is decreasing function on the inter...

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  8. Show that function f(x)=sin(2x+pi/4) is decreasing on ((3pi)/8,(5pi)/8...

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  9. Show that f(x)=x-sinx is increasing for all x in R

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  10. Find the value(s) for a for which f(x)=x^3-a x is an increasing functi...

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  11. Find the intervals in which function f(x) = sin x-cos x, 0 lt x lt 2pi...

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  12. Determine the values of x for which the function f(x)=x^2-6x+9 is incr...

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  13. Find the intervals in which the following function are increasing or ...

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  14. Show that f(x)=e^(1/x),x!=0 is decreasing function for all x!=0.

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  15. Show that f(x)=e^(2x) is increasing on Rdot

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

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

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

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

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

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