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    Hey guys. Would anyone tell me some reasoning to the following problems/topics. I'm still really struggling to understand them. Thanks so much.


    1)

    y^2(is bigger or equall to)4y+5

    So I have solutions y=-1 and y=5 but why does it have to be put into the form:
    y(is smaller or equal to)-1 and y(is bigger or equal to 5. I don't understand which way round the signs should be and whether they are two seperate ones or put into the same inequality.


    2) Find the value of c which the line y=x+c is a tangent to the curve y=x^2-5x+4. Previously there has been two simultaneous equations (y=x^2-5x+4 and y=x-1 which i have solved for solutions (5,4) and (1,0) and there are two points of intersection that i found.

    I've been told i need to put the y=x+c into the y=x-1 then equal that to the curve equation and then do b^2-4ac. Could you elaberate(?) on what she means here please?
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    [QUOTE=Robpattinsonxxx;28798801]Hey guys. Would anyone tell me some reasoning to the following problems/topics. I'm still really struggling to understand them. Thanks so much.


    1)

    y^2(is bigger or equall to)4y+5

    So I have solutions y=-1 and y=5 but why does it have to be put into the form:
    y(is smaller or equal to)-1 and y(is bigger or equal to 5. I don't understand which way round the signs should be and whether they are two seperate ones or put into the same inequality.QUOTE]

    Because if -1 < y < 5 then the statement (y^2(is bigger or equall to)4y+5) won't be correct. You can try to calculate both sides with 4,5 and -05 and you'll see that it wont be correct. Well the signs shouldn't be two separate ones since it is for the same inequality.

    That's all I can help you with I'm afraid...didn't really understand the second problem. If you could post the entire question as it is written in the book it will be easier to answer...
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    For your second question.

    The line y=x+c has a gradient of 1. It will be a tangent to the curve at the point where the curve has a gradient of 1.



    Alternatively, following the hint your teacher gave, sub in x+c for y in y=x^2-5x+4, rearrange, find the determinant and set it equal to zero.
 
 
 
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