Posted by Stephen on Monday, January 14, 2013 at 11:33pm.
1. The curve y=10/2x+1 2 intersects the xaxis at A. The tangent to the curve at A intersects the yaxis at C.
(i) Show that the equation of AC is 5y+4x=8
(ii) Find the distance of AC
2. The equation of a curve is y=1/6(2x3)^34x
(i) Find dy/dx
(ii) Find the equation of the tangent to the curve at the point where the curve intersects the yaxis.

Math  Steve, Tuesday, January 15, 2013 at 12:00pm
the curve intersects the xaxis at (2,0)
y'(x) = 20/(2x+1)^2
y'(2) = 4/5
tangent at (2,0) is
y = 4/5 (x2)
intersects the yaxis at (0,8/5)
AC is thus
y = (x2)(4/5)
5y = 84x
5y+4x=8

y = 1/6 (2x3)^3  4x
y' = (2x3)^2  4
the curve has yintercept at (0,9/2)
y'(0) = 5
so, the line is
y+9/2 = 5x
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