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The function f(x)=(ln(pi+x))/(ln(e+x)) i...

The function `f(x)=(ln(pi+x))/(ln(e+x))` is increasing in `(0,oo)` decreasing in `(0,oo)` increasing in `(0,pi/e),` decreasing in `(pi/e ,oo)` decreasing in `(0,pi/e),` increasing in `(pi/e ,oo)`

A

Increasing on `[0,infty)`

B

Decreasing on `[0,infty)`

C

Decreasing on `[0,pi/e)` and increasing on `[pi/e,infty)`

D

Increasing on `[0,pi/e)` and decreasing on `[pi/e,infty)`

Text Solution

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The correct Answer is:
B
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TARGET PUBLICATION-APPLICATIONS OF DERIVATIVES-COMPETITIVE THINKING
  1. The function f defined by f(x)=(x+2)e^(-x) is

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  2. A function is matched below against an interval where it is supposed t...

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  3. The function f(x)=(ln(pi+x))/(ln(e+x)) is increasing in (0,oo) decrea...

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  4. If f(x)=x^3-10 x^2+200 x-10, then f(x) is

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  5. If f(x)=x^(3/2)(3x-10),xgeq0, then f(x) is increasing in .

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  6. The function f(x)=tan^(-1)(sinx+cosx) is an increasing function in

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  7. Let f(x) = log (sin x+ cos x), x in x (-pi/4,(3pi)/(4)) . Then f is st...

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  8. Let f(x)=inte^x(x-1)(x-2)dxdot Then f decreases in the interval (-oo,...

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  9. f(x)=(x)/(sinx ) and g(x)=(x)/(tanx) , where 0 lt x le 1 then in the...

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  10. If f(x)=sinx-cosx, the function decreasing in 0 le x le 2pi is

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  11. Let h(x)=f(x)-(f(x))^2+(f(x))^3 for every real x. Then,

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  12. The function f(x)=[x(x-2)]^2 is increasing in the set

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  13. y=x(x-3)^2 increases for all values of x lying in the interval

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  14. The minimum value of f(a)=(2a^2-3)+3(3-a)+4 is

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  15. The value of a for which the function f(x)=asinx+(1/3)sin3x has an ext...

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  16. The function x^(5)-5x^(4)+ 5x^(3) -10 has a maxima, when x=

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  17. If for a function f(x),f'(a)=0,f"(a)=0,f'''(a)gt0, then at x=a,f(x) is

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  18. The local maximum of y=x^3-3x^2+5 is attained at

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  19. The function f(x)=2x^3-15 x^2+36 x+4 is maximum at

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  20. Let f(x)=2x^3-3x^2-12 x+5 on [-2,\ 4] . The relative maximum occurs ...

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