Finding the derivative of f.

[Fiestar]

Find the derivative of f(x) = {sin(1-2x), if x < 1; 0, if x = 1; x^2, if x > 1}
The thing is we have to prove it as well using the derivative definition f'(a) = lim (x->a) (f(x) - f(a))/x-a and I am having problems showing sin(1-2x).

 

[tkhunny]

Is this piecewise function? You may wish to prove first if it is continuous t the internal boundaries.

Please write out your expression for the sine function. Let' see how close you get.

Note: Something/x-c is NOT the same as Something/(x-c)

 

[Fiestar]

 

[tkhunny]

That's a lot of work before you even know if it's continuous.


What's the chance you can use the other definition? \(\displaystyle f'(x) = \lim\limits_{h\to 0}\dfrac{f(x+h) - f(x)}{h}\)

 

[Fiestar]

I will try the other one then, didn't think about that one

 

[tkhunny]

Seems to be a lot less trouble. Good work.