Discussion:
the given curve
(too old to reply)
spiny urchin
2015-07-25 22:40:13 UTC
Permalink
Raw Message
With the given curve, I've tried to find the normal and tangents, but
haven't succeeded yet, except by qualitatively reading the data off of the
graph:

http://www.stonetabernacle.com/graph-of-a-curve-II.html
William Elliot
2015-07-26 02:38:10 UTC
Permalink
Raw Message
With the given curve, I've tried to find the normal and tangents, but haven't
For a given curve y = f(x), the slope of the tangent for x = a
is f'(a) and the slope of the normal is -1/f'(a). The tangent at x = a
is the line through (a,f(a)) with the slope of f'(a) and the normal at x = a
is the line through (a,f(x)) with the slope of -1/f'(a).

The equation of a line through (a,b) with the slope of m is
y - b = m(x - a). f'(x) = df(x)/dx = derivative of f at x.

What's the equation of your curve? Is it given explicity
in the form of y = f(y) or inplicity in the form of g(x,y) = 0
for some two valued function g?
Virgil
2015-07-26 03:57:20 UTC
Permalink
Raw Message
Post by William Elliot
With the given curve, I've tried to find the normal and tangents, but haven't
For a given curve y = f(x), the slope of the tangent for x = a
is f'(a) and the slope of the normal is -1/f'(a). The tangent at x = a
is the line through (a,f(a)) with the slope of f'(a) and the normal at x = a
is the line through (a,f(x)) with the slope of -1/f'(a).
Minor typo! The normal at x=a is a line through (a,f(a)).
Post by William Elliot
The equation of a line through (a,b) with the slope of m is
y - b = m(x - a). f'(x) = df(x)/dx = derivative of f at x.
What's the equation of your curve? Is it given explicity
in the form of y = f(y) or inplicity in the form of g(x,y) = 0
for some two valued function g?
--
Virgil
"Mit der Dummheit kampfen Gotter selbst vergebens." (Schiller)
Loading...