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    please help me on this:

    the diagram (Name:  curveABC.png
Views: 147
Size:  7.4 KB) shows part of the curve, y=x^2 + 5. the point A has coordinates (1,6). the point B has coordinates(a,a+5) where a is a constant greater than 1. the point C is on the curve between A and B.

    i) find by differentiation the value of the gradient of the curve at the point A.
    i was able to do this part only. my answer was '2'.

    ii) the line segment joining the points A and B has gradient '2.3'. find the value of a.

    iii) state a possible value for the gradient of the line segment joining the points A and C.
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    (Original post by cooldudeman)
    please help me on this:

    the diagram (Name:  curveABC.png
Views: 147
Size:  7.4 KB) shows part of the curve, y=x^2 + 5. the point A has coordinates (1,6). the point B has coordinates(a,a+5) where a is a constant greater than 1. the point C is on the curve between A and B.

    i) find by differentiation the value of the gradient of the curve at the point A.
    i was able to do this part only. my answer was '2'.

    ii) the line segment joining the points A and B has gradient '2.3'. find the value of a.

    iii) state a possible value for the gradient of the line segment joining the points A and C.
    For (ii) When you're looking for the gradient of a line between two points (x_1,y_1), (x_2,y_2), the gradient m = \frac{y_2-y_1}{x_2-x_1}.
    For (iii) Think about what happens to the line segment as B moves down the curve towards A. Is the gradient getting more steep or less steep? Give an answer accordingly.
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    (Original post by Farhan.Hanif93)
    For (ii) When you're looking for the gradient of a line between two points (x_1,y_1), (x_2,y_2), the gradient m = \frac{y_2-y_1}{x_2-x_1}.
    For (iii) Think about what happens to the line segment as B moves down the curve towards A. Is the gradient getting more steep or less steep? Give an answer accordingly.
    for ii, i substituted the values from the graph.
    (a^2 +5-6)/a-1
    a^2 -1/a -1
    a+1=2.3
    a=1.3
    am i correct?

    but for iii, i still dont get it. it would get less steep and the gradient would decrese but i dont know how to get an exact value... can the answer be in an inequalitie?
 
 
 
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