hi, i am very confused on this topic and my teacher hasn't explained it well. could i have some help please understanding this.
3 g(x) = 10 - 2x - x ^ 2
a Find the equation of the tangent to the curve y = g(x) at the point where x = 1 .
b Find the equation of the normal to the curve y = g(x) at the point where x = 1 .
E4 f(x) = x ^ 2 - 5x + 4
a Find the equation of the tangent to the curve y = f(x) at the point where x = 5
(3 marks)
b Find the equation of the normal to the curve y = f(x) at the point where x = 3
(3 marks)
The tangent found in part a intersects the normal found in part b at the point P. e Find the coordinates of point P.
(4 marks)
E 5 g(x) = x ^ 3 - 4x
a Find the equation of the tangent to the curve y = g(x) at the point where x = - 1 .
(3 marks)
This tangent meets the x-axis at the point A.
b Find the coordinates of A.
(1 mark)
e Show that A lies on the curve y = g(x)
(1 mark)
E/P 6 The point P with x-coordinate 6 lies on the curve with equation y = 1/2 * x ^ 2 - 8x + 6
The normal to the curve at P intersects the curve at the points P and Q.
Find the coordinates of Q