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This is the drawback of being self taught. When your stuck you can't ask teacher.
So you can spot it on a graphing calculator if it has a corner point or cusp?
If you can use a graphing calculator, you can spot non-differentiable parts at a point if:
I'm not sure what you mean. That must be above my level. This is calculus 1. I have no idea what "matrix of partial derivative" is.
f(t) = ( 4 cos(t) - 4 cos(4t) , 4 sin (t) - 4 sin(4t) )
where Df(x0) is the matrix of partial derivatives. In this case:
Df = ( 16sin(4t) - 4sin(t) , 4cos(t) - 16cos(4t) )
Since there is only one variable in this function, there are no partials.
Try using that definition to see if it works.
Ok right. I got it backwards.
If a function is differentiable, then it is continuous.
But consider the function f(x) = |x|. It is continuous at 0, but not differentiable.
Doesn't continuity imply differentiability?
You want differentiability, not continuity. I'm still working on this problem though.
you can only integrate using the arc length formula to find the length of a curve if the curve is continuous on the given interval. If their is a sharp point at b between a and c, you need to integrate from a to b, then b to c. a to c won't work since the function must be continuous to integrate.