Quantcast
Channel: Active questions tagged real-analysis - Mathematics Stack Exchange
Viewing all articles
Browse latest Browse all 9183

Which one of the following is TRUE(Real Analysis)? [closed]

$
0
0

Let $$f(x) =\begin{cases}x+1&x<0\\(x-1)^2&x≥0.\end{cases}$$Which one of the following is true?

(a) f is differentiable on R

(b) f has neither a local maximum nor a local minimum in R

(c) f is bounded on R

(d) f is not differentiable at x =0 and f(x) has local maximum at x = 0.

I know how f(x) is not differentiable at x = 0 but I'm not getting local maximum at x = 0.When I differentiate f(x) at x<0,f'(x)= 1,but when I differentiate when x>0,f'(x) = 2(x-1).

2(x-1)=0so, x = 1f''(x)= 2so, x=1 is a local minimum.


Viewing all articles
Browse latest Browse all 9183

Trending Articles



<script src="https://jsc.adskeeper.com/r/s/rssing.com.1596347.js" async> </script>