CALCULUS Understanding Its Concepts and Methods

Tangent lines

The tangent
line to a curve at a point *P* on the curve is the straight line through
*P* that best
approximates the curve near *P*.

If *f'*(*a*)
exists, then the tangent line to the graph of *f*(*x*) at the point (*a*,*f*(*a*)) is
the line *y* = *f*(*a*)
+ *f'*(*a*)(*x* - *a*).

If *x**'*(*a*) and *y'*(*a*) exist, then
the tangent line to the parametric curve (*x*(*t*),*y*(*t*))
at the point (*x*(*a*),*y*(*a*)) is the line (*x*(*a*) + *t**x**'*(*a*),*y*(*a*) + *ty'*(*a*)).

If *x**'*(*a*) = 0 and *y'*(*a*) ≠ 0, then the
tangent line is vertical.

If *x**'*(*a*) ≠ 0 and *y'*(*a*) = 0, then the
tangent line is horizontal.

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Copyright © 2006 Darel Hardy, Fred Richman, Carol Walker, Robert Wisner. All rights reserved. Except upon the express prior permission in writing, from the authors, no part of this work may be reproduced, transcribed, stored electronically, or transmitted in any form by any method.