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Without using the dervative, show that f...

Without using the dervative, show that f(x) = |x| is strictly decreasing in `(-infty,0)`

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MODERN PUBLICATION-APPLICATION OF DERIVATIVES-EXERCISE
  1. Show that the following functions are strictly increasing on R: f(x) =...

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  2. Without using the dervative, show that f(x) = |x| is strictly increasi...

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  3. Without using the dervative, show that f(x) = |x| is strictly decreasi...

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  4. Show that the function f given by, f(x) = x^3 - 3x^2 + 4x, x in R is i...

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  5. Show that the function f(x) = x^3-6x^2 + 15x + 4 is strictly increasin...

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  6. Prove that : f(x) = x^2 is a decreasing function for x < 0, where x in...

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  7. Prove that f(x) = 3/x + 7 is strictly decreasing for x in R-{0}.

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  8. Prove that the function given by f(x) = x^3 - 3x^2 + 3x - 100 is incre...

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  9. Prove that f(x) = 4x^3 - 6x^2 + 3x + 12 is strictly increasing functio...

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  10. f(x) = cos x is strictly decreasing in (0, pi)

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  11. f(x) = cos x is strictly increasing in (pi,2pi)

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  12. f(x) = cos x is neither increasing nor decreasing in (0,2pi)

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  13. f(x) = sin x is a strictly increasing in (0, pi/2)

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  14. f(x) = sin x is a strictly decreasing in (pi/2,pi)

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  15. Show that the function given by f(x) = sinx is neither increasing no...

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  16. Prove that f(x) = 2 sinx + 1 is an increasing function on [0,pi/2]

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  17. f(x) = tan^-1(sinx+cosx) is strictly decreasing function on (pi/4,pi/2...

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  18. Prove that the logarithmic function is increasing on (0,∞).

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  19. Prove that the function f given by f(x) = log sin x is strictly increa...

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  20. Prove that f(x)="log""cos"x is strictly decreasing on (0,pi/(2)) and s...

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