equations of tangents and normals

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

Reply 1

mqb2766

Original post by Gracefully1234

A tangent to a curve at a point is a line which touches the curve at that point. So it has the same (x,y) value and the same gradient. So just evaulate the point (x,y) and the gradient of the curve at that point and that gives the line (tangent).

A normal (line) is similar but itis perpendicular to the tangent. So get the point and gradient as before then work out the perpendicular gradient.

https://mathcentre.ac.uk/resources/uploaded/mc-ty-tannorm-2009-1.pdf

Have a go and post what youve tried if youre unsure?