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Math Help - Derivative and Graph shape questions

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    Derivative and Graph shape questions

    I need help bad. I just can't seem to get these problems. Any help would be greatly appreciated.

    1. a)Find the intervals on which f is increasing or decreasin
    b)Find the local maximum and minimum values of f
    c)Find the intervals of concavity and the inflection points

    f(x)=(x^2) / ((x^2) + 3)

    2.Find the limit using l'Hospital's rule where appropriate unless it's easier another way.


    lim (as tapproaches 0) ((e^3t)-1) / t

    3.^^^Same as 2^^^

    lim (as x approaches infinity) (xe^(1/x)) - x
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  2. #2
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    Quote Originally Posted by Subby07 View Post
    I need help bad. I just can't seem to get these problems. Any help would be greatly appreciated.

    1. a)Find the intervals on which f is increasing or decreasin
    b)Find the local maximum and minimum values of f
    c)Find the intervals of concavity and the inflection points

    f(x)=(x^2) / ((x^2) + 3)

    2.Find the limit using l'Hospital's rule where appropriate unless it's easier another way.


    lim (as tapproaches 0) ((e^3t)-1) / t

    3.^^^Same as 2^^^

    lim (as x approaches infinity) (xe^(1/x)) - x
    for 2 by L'hospital's rule

    \lim_{t \to 0}\frac{e^{3t}-1}{t}=\lim_{t \to 0}\frac{3e^{3t}}{1}=3

    for 3


    \lim_{x \to \infty}x(e^{1/x}-1)=\frac{e^{1/x}-1}{1/x}

    The second is in the form for L.H 0/0

     \lim_{x \to \infty} \frac{e^{1/x}-1}{1/x}=\frac{\frac{-1}{x^2}e^{1/x}}{\frac{-1}{x^2}}=e^{1/x}=1
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