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Math Help - Finding most steep slope

  1. #1
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    Finding most steep slope

    Consider the function f (x) = √x + 1/3x
    This function forms the curve of a cross section of a flower. A small insect is stuck inside the flower and keeps trying to walk up either side. At which of the following is the slope most difficult to walk up, or most steep.
    a. x = 0.5
    b. x = 1
    c. x = 4
    d. x = 9

    I was wondering if anyone can tell the answer and explain it to me please.
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  2. #2
    Senior Member apcalculus's Avatar
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    Quote Originally Posted by Hakhengkim View Post
    Consider the function f (x) = √x + 1/3x
    This function forms the curve of a cross section of a flower. A small insect is stuck inside the flower and keeps trying to walk up either side. At which of the following is the slope most difficult to walk up, or most steep.
    a. x = 0.5
    b. x = 1
    c. x = 4
    d. x = 9

    I was wondering if anyone can tell the answer and explain it to me please.

    Find the first derivative; then plug in the given x-values. The resulting derivative values measure SLOPE at those four points. whichever is the bigger value (in absolute value) is the steepest location.

    Good luck!!
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