The line has equation y=2x+c and a curve has equation y=82xx^2.
1) for the case where the line is a tangent to the curve, find the value of the constant c.
2) For the case where c = 11, find the xcoordinates of the points of intersection of the line and the curve. Find also, by integration, the area of region between the line and the curve.
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2 answers

to solve:
2x+c = 82xx^2
x^2 + 4x + c8 = 0
to have y = 2x+c to be a tangent, there can be only one real root of the quadratic
so b^2  4ac = 0
16  4(1)(c8) = 0
16  4c + 32 = 0
4c = 48
c = 48/4 = 12
check with Wolfram:
http://www.wolframalpha.com/input/?i=y%3D2x%2B12,+y%3D82xx%5E2
for your second part
y = 2x+11, y = 82x  x^2
I will let you solve it to show:
http://www.wolframalpha.com/input/?i=y%3D2x%2B11,+y%3D82xx%5E2
so for the area:
A = ∫ (82xx^2  2x  11) dx from 3 to 1
simplify and finish it
this looks very straightforward, I trust you can handle it 👍
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No it isnt that straightforward u must take into account the area of the trapezium as well so the best thing to do is to draw out the diagram
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