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The curvey y=f(x) which satisfies the co...

The curvey y=f(x) which satisfies the condition `f'(x)gt0andf''(x)lt0`m for all real x, is

A

B

C

D

Text Solution

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The correct Answer is:
D
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Knowledge Check

  • Let f'(x) gt0 and g'(x) lt 0 " for all " x in R Then

    A
    `f{g(x)gtf(g(X+1)}`
    B
    `f{g(x)gtf(g(X-1)}`
    C
    `g{f(x)gtg(f(X+1)}`
    D
    `g{f(x)gtg(f(X-1)}`

  • If f:RtoR is a function which satisfies the condition f(x)+f(y)=f((x+y)/(1+xy)) for all x, y in R except xy=-1 , then range of f(x) is

    A
    `[0,infty)`
    B
    `{0,1}`
    C
    `R`
    D
    `{0}`

  • A continuous and differentiable function f satisfies the condition, int_(0)^(x)f(t)dt=f^(2)(x)-1 for all real x. Then

    A
    f is monotonic increasing `AA x in R`
    B
    f is monotonic decreasing `AA x in R`
    C
    f is non monotonic
    D
    the graph of `y=f(x)` is a straight line

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    Let f(x) be a quadratic expression which is positive for all real x and g(x)=f(x)+f'(x)+f''(x) .A quadratic expression f(x) has same sign as that coefficient of x^2 for all real x if and only if the roots of the corresponding equation f(x)=0 are imaginary. For function f(x) and g(x) which of the following is true (A) f(x)g(x)gt0 for all real x (B) f(x)g(x)lt0 for all real x (C) f(x)g(x)=0 for some real x (D) f(x)g(x)=0 for all real x

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