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    Hey, I keep getting the wrong answer for this question, taken from the C2 book (pg. 134, ex. 9B)…it’s number 3g: Find the coordinates of the points where the gradient is zero on the curves with equation y=3* sqrt x (not small 3 inside x, but 3*sqrtx). Establish whether these points are maximum, minimum or points of inflexion, by considering the second derivative.

    Also, number 5: By considering the gradient on either side of the stationary point on the curve y=x^3-3x^2+3x, show that this point is a point of inflexion. (And then sketch the curve y=x^3-3x^2+3x)
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    (Original post by *girlie*)
    Hey, I keep getting the wrong answer for this question, taken from the C2 book (pg. 134, ex. 9B)…it’s number 3g: Find the coordinates of the points where the gradient is zero on the curves with equation y=3* sqrt x (not small 3 inside x, but 3*sqrtx). Establish whether these points are maximum, minimum or points of inflexion, by considering the second derivative.

    Also, number 5: By considering the gradient on either side of the stationary point on the curve y=x^3-3x^2+3x, show that this point is a point of inflexion. (And then sketch the curve y=x^3-3x^2+3x)
    y=3rtx has no stationary points ?

    Question 5,
    dy/dx = 3x^2 - 6x + 3
    0 = 3x^2 - 6x + 3
    0=x^2 - 2x + 1 = (x-1)^2 => x=0 is a stationary point.
    When x=0.1, y=0.271
    When x = -0.1, y = -0.331
    Because its negative one side of the stationary point, and positve the other, it must be a point of inflection.
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    (Original post by [email protected])
    y=3rtx has no stationary points ?

    Question 5,
    dy/dx = 3x^2 - 6x + 3
    0 = 3x^2 - 6x + 3
    0=x^2 - 2x + 1 = (x-1)^2 => x=0 is a stationary point.
    When x=0.1, y=0.271
    When x = -0.1, y = -0.331
    Because its negative one side of the stationary point, and positve the other, it must be a point of inflection.
    yeah, it does have stationary points...the Q is asking to find them (coords), isn't it? I got all the other Qs right, just can't do this one, for some reason!

    Thanks for Q5
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    Plot y = 3x^1/2 and you'll see it doesn't.
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    (Original post by [email protected])
    Plot y = 3x^1/2 and you'll see it doesn't.
    Oh. And isn't it y=x-3x^1/2?
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    You typed
    "y=3* sqrt x" I've not got the book here
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    (Original post by [email protected])
    You typed
    "y=3* sqrt x" I've not got the book here
    whoops, sorry. It's y=x-3sqrtx
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    (Original post by *girlie*)
    Oh. And isn't it y=x-3x^1/2?
    y=x-3x^1/2
    dy/dx = 1-1.5/x^1/2
    0 = 1-1.5/x^1/2
    1= 1.5/x^0.5
    x^0.5 = 1.5
    x = 2.25
    d^2/dx^2 = 0.75x^-(3/2)
    substituing x=2.25, gives d^2/dx^2 = 0.22222 > 0 => minimum
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    (Original post by [email protected])
    y=x-3x^1/2
    dy/dx = 1-1.5/x^1/2
    0 = 1-1.5/x^1/2
    1= 1.5/x^0.5
    x^0.5 = 1.5
    x = 2.25
    d^2/dx^2 = 0.75x^-(3/2)
    substituing x=2.25, gives d^2/dx^2 = 0.22222 > 0 => minimum
    ohh thanks, i get it now!
 
 
 
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