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    If it says prove a curve has no turning points when they give you its forumula

    and you differentiate it and say you get 3x^2 + 2,

    to show it has no turning points is all you do just put a line through an equal sign and put 0 next to it i.e 3x^2 + 3 not equal to 0

    or is there some mathematical way of proving it?!

    this is for a/o maths tommorow
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    Your reasoning is fine, but I'd recommend you write it a bit clearer than that. Write a sentence like "3x^2 + 2 is nonzero for all real values of x, so the gradient of the curve is never 0 and hence there are no turning points".
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    Ok, so dy/dx= 3x^2+2

    At turning points or stationary points, dy/dx=0

    so... 3x^2 + 2 = 0
    3x^2 = -2
    x^2 = -2/3
    x = square root of -2/3

    but you cant square root a negative number because square numbers are always positive...so there are no solutions for dy/dx=0 therefore no stationary points
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    Thanks So much!
 
 
 
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