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Math Help - small confusion in increasing/decreasing function

  1. #1
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    small confusion in increasing/decreasing function

    A> if a function is f(x) defined in R--> R, STRICLTY increasing and differentiable.. then the derivative of f:
    a. May be less than 0 at some x.
    b. May be infinite at some x.
    c. is greater than or equal to 0 at every x belonging to R
    d. is greater than 0 at every x belonging to R

    I think the answer is "d" but I am not too sure as it can be 0 also at some point? This is because the second question has confused me a bit.

    =-===========================
    B> Consider a strictly decreasing function which is differentiable. Which of the following "may be true" about the derivative of f.

    a. derivative > 0 for some x belonging to R
    b. derivative = 0 for some x belonging to R
    c. derivative = 0 for every x belonging to (a,b) where a<b.
    d. derivative >= 0 for every x belonging to R

    i think the ideal answer should have been "less than 0" but since that option is not there at all, i am slightly confused.
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  2. #2
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    [QUOTE=champrock;220156]A> if a function is f(x) defined in R--> R, STRICLTY increasing and differentiable.. then the derivative of f:
    a. May be less than 0 at some x.
    b. May be infinite at some x.
    c. is greater than or equal to 0 at every x belonging to R
    d. is greater than 0 at every x belonging to R

    I think the answer is "d" but I am not too sure as it can be 0 also at some point? This is because the second question has confused me a bit.[quote]
    Consider the function f(x)= x^3.

    =-===========================
    B> Consider a strictly decreasing function which is differentiable. Which of the following "may be true" about the derivative of f.

    a. derivative > 0 for some x belonging to R
    b. derivative = 0 for some x belonging to R
    c. derivative = 0 for every x belonging to (a,b) where a<b.
    d. derivative >= 0 for every x belonging to R

    i think the ideal answer should have been "less than 0" but since that option is not there at all, i am slightly confused.
    Now look at f(x)= -x^3.
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  3. #3
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    got it.

    was not taking the inflection points into consideration

    thanks a tonne
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