evaluation of slope & curvature

sofiya

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Oct 21, 2014
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Please anyone could help me with this? I need a good start, trying to understand. thanks so much.

a) Given a curve y = f(x) in a Cartesian (x, y) plane, describe the evaluation of its
slope at any point xo.


b) Given a curve y = f(x) in a Cartesian (x, y) plane, describe the evaluation of its
curvature at any point xo.

Thanks,
Sofiya
 
What course is this for? You posted this in "Geometry and Trig" but these are Calculus problems. The slope of the tangent line at any point on the graph of a function is its derivative there, f'(x). The curvature is given by the second derivative though not just the second derivative itself. For y= f(x), the curvature is given by \(\displaystyle \frac{f''(x)}{(1+ (f'(x))^2)^{3/2}}\).

If you are taking Calculus, surely those formulas are in your textbook?
 
What course is this for? You posted this in "Geometry and Trig" but these are Calculus problems. The slope of the tangent line at any point on the graph of a function is its derivative there, f'(x). The curvature is given by the second derivative though not just the second derivative itself. For y= f(x), the curvature is given by \(\displaystyle \frac{f''(x)}{(1+ (f'(x))^2)^{3/2}}\).

If you are taking Calculus, surely those formulas are in your textbook?


Thank you for that, I dont know even where to start. i wish i had your brains HallsofIvy :)
 
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