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# very confusing question Watch

the diagram () 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.
2. (Original post by cooldudeman)

the diagram () 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 , the gradient .
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.
3. (Original post by Farhan.Hanif93)
For (ii) When you're looking for the gradient of a line between two points , the gradient .
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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Updated: December 6, 2010
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