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Math Help - Help me verify my work !

  1. #1
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    Exclamation Help me verify my work !

    I have some questions due tomorrow, and I'd really like to know if the answers are right.

    1) f(x)=2x^3-4x^2-10x+12
    Find the intervals where f(x) is
    a) concave up  2/3 to positive infinity
    b) concave up negative infinity to  2/3
    c) Find all inflection points (2/3, 3.852)

    2) Write the equation(s) of the vertical tangent(s) to the curve y^3-3xy=2
    y=-1 and x=1


    Also, I have NOOoOOO clue how to do this problem:
    A square is inscribed in a circle as shown below (ignore the circle with the triangle). As the square expands, the circle expands to maintain the four points of intersection. The perimeter of the square is increasing at the rate of 12 in/second.

    a) Write the circumference of the circle as a function of the side of the square:
    C(s)=2pi(s/squareroot of 2)
    b) Find the rate at which the circumference of the circle is increasing
    c) At the instant when the area of the square is 16 square inches, find the rate at which the area enclosed between the square and the circle is increasing.
    d) The radius of a circle is decreasing at a constant rate of .2cm/s. In terms of circumference, what is the rate of change of the area of the circle?

    thank you!!
    Last edited by NoiseandAttack; December 9th 2007 at 03:21 PM. Reason: pressed enter by accident before finishing post.. sorry!
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  2. #2
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    please help with the circle problem :[
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  3. #3
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    Quote Originally Posted by NoiseandAttack View Post
    2) Write the equation(s) of the vertical tangent(s) to the curve y^3-3xy=2
    y=-1 and x=1
    Yes the vertical tangent is x=1.
    Attached Thumbnails Attached Thumbnails Help me verify my work !-vertical-tangent.gif  
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  4. #4
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    Quote Originally Posted by NoiseandAttack View Post
    1) f(x)=2x^3-4x^2-10x+12
    Find the intervals where f(x) is
    a) concave up  2/3 to positive infinity
    b) concave up negative infinity to  2/3
    c) Find all inflection points (2/3, 3.852)
    Yes you are right.
    Attached Thumbnails Attached Thumbnails Help me verify my work !-concave-up.gif  
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