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Gradients of tangents, Equation of tangent and Normal<br />
If A(x1, y1) is a point on a line y = f(x), the gradient<br />
of the line (for a straight line) or the gradient of the<br />
tangent of the line (for a curve) is the value of dy<br />
dx<br />
when x = x1.<br />
Maximum and Minimum Point<br />
At maximum point,<br />
dy<br />
0<br />
dx =<br />
2<br />
d y<br />
2<br />
0<br />
dx <<br />
http://www.one-school.net/notes.html<br />
dy<br />
Turning point ⇒ 0<br />
dx =<br />
12<br />
Gradient of tangent at A(x1, y1):<br />
dy<br />
dx =<br />
ONE-SCHOOL.NET<br />
gradient of tangent<br />
Equation of tangent: y− y1 = m( x− x1)<br />
Gradient of normal at A(x1, y1):<br />
m<br />
normal<br />
1<br />
=−<br />
m<br />
tangent<br />
1<br />
= gradient of normal<br />
−<br />
dy<br />
dx<br />
Equation of normal : y − y1 = m( x− x1)<br />
At minimum point ,<br />
dy<br />
0<br />
dx =<br />
2<br />
d y<br />
2<br />
0<br />
dx >
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