- #1
Claire84
- 219
- 0
If f is a function defined by the fomula f(x)=xe^(modx), then show that f is differentiable at every point c, with
f'(c)=(mod(c) +1)e^(modx)
The hint that is given is 'consider separately the cases cgreater than 0, c less than 0 and c=0
To prove that f is differemtiable at every point c, do I have to have f as 2 seorate functions mmultiplied together, and if each of them is differentiable then does it mean that f is differentiable? I tried this and it was fimne fpr the function equal to x, but I couldn't work it out for the function equal to e^(modx) . Is there a better way of proving that it is differentiable?
Also, is there a reason why we have mod(c) inside the brakcets of f'(c) as opposed to just c?
f'(c)=(mod(c) +1)e^(modx)
The hint that is given is 'consider separately the cases cgreater than 0, c less than 0 and c=0
To prove that f is differemtiable at every point c, do I have to have f as 2 seorate functions mmultiplied together, and if each of them is differentiable then does it mean that f is differentiable? I tried this and it was fimne fpr the function equal to x, but I couldn't work it out for the function equal to e^(modx) . Is there a better way of proving that it is differentiable?
Also, is there a reason why we have mod(c) inside the brakcets of f'(c) as opposed to just c?