Solve the complete Equation ?

Question

A curve has the equation y = x/2 + 3 - 1/x , x is not equal to 0

the point A on the curve has x coordinate 2

(a) find the gradient of the curve at A

(b) show that the tangent to the curve at A has equation 3x - 4y + 8 = 0

the tangent to the curve at the point B is parallel to the tangent at A

(c) find the coordinates of B

Answer 1

I agree with Ron W's answer.  It is 100% accurate

ANSWER

Answer 2

(a)

y' = 1/2 + 1/x²

y'(2) = 3/4

(b)

y(2) = 7/2

Tangent line equation:

y - 7/2 = (3/4)(x - 2)

4y - 14 = 3x - 6

0 = 3x - 4y + 8

(c)

If the tangent line is parallel to the one found in (b), then it has the same slope. So

1/2 + 1/x² = 3/4

1/x² = 1/4

x² = 4

x = ± 2

So the coordinates of B are (-2, 5/2)