1. Find the equation of the tangent to the curve y = x² + 4 at the point where x = 2.

2. Find the equation of the tangent to the graph of the cubic y = x³ − 2x² + 2x + 4 at the point (1, 5). What is the equation of the normal to this curve at this point?

3. Find the equations of the tangents at the points (1/2 , 1) and (2, −2) to the parabola y² = 2x What are the co-ordinates of the point of intersection of these two tangents?

4. Find the equation of the tangent to the graph of y = x³ − x² at the point (1, 0). What is the equation of the normal at this point?

5. The two points P and Q lie on the curve y² = 4x and have co-ordinates (1, −2) and (9, 6) respectively. Find

(a) The equation of the tangent at the point P.

(b) The equation of the normal at the point Q.

(c) If the tangent and normal intersect at the point R, find the co-ordinates of R.

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[Reminder: (slope of normal)= -1/ (slope of tangent)]