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Increasing and decreasing Functions...

Increasing and decreasing Functions

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Knowledge Check

  • Let f(x) = (x)/(sqrt(a^(2) + x^(2)))- (d-x)/(sqrt(b^(2) + (d-x)^(2))), x in R , where a, b and d are non-zero real constants. Then, (A) f is an increasing function of x (B) f' is not a continuous function of x (C) f is a decreasing function of x (D) f is neither increasing nor decreasing function of x

    A
    `f` is an increasing function of x
    B
    `f'` is not a continuous function of x
    C
    `f` is a decreasing function of x
    D
    `f` is neither increasing nor decreasing function of x

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    (a) Find the intervals in which the function f(x)=log(1+x)-x/(1+x) is (i) increasing, (ii) decreasing function. (b) Find the intervals in which the function f(x)= x/(log_(e) x),x gt 0 is increasing or decreasing.

    Statement 1 The equation a^(x)+b^(x)+c^(x)-d^(x)=0 has only real root, if agtbgtcgtd . Statement 2 If f(x) is either strictly increasing or decreasing function, then f(x)=0 has only real root.

    Find the interval of increasing and decreasing of the function f(x) =(log x)/(x)

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