Question

Question 1 20 points Save Answer Mark all true statements (there might be more than one statement that is true). 2 3 Let f: RR be given by f(x)=x Then X=0 is a critical point of f.. Let f:ASR-R and assume that fis differentiable at XoeInt(A) and Xo is a O local extreme point. Then f(x)=0. Let f: (a,b) -R be differentiable on (a,b) and f(c)>0, where ce(a,b). Then there is 6>0, such that, for all x,y ED(0,6)n(a,b), if x <y then f(x)<fly). Let f: ASR +R be differentiable at CEInt(A) then there is M20 and 6 >0 such that for all X ED(0,6) NA, \f(x)] SM. Let f: R+R be given by f(x) = sin(x) ifx so -X if x>0 then f is differentiable at x=0.

Answer 1

2 hla 23 Noiz (IC but ato so'ra)=şx-13 f'(x)=0 false, n=0 not a critical Point of s.

2 If local entremum exist then filno) o True

le 5(2) - $(7) yo jie stessa. Sess, scal-sly ricoh lon sa j'(c) > is acy -> Sca) CSP) (True)

pa sophre) x-@ 2 p es differentiable at ac A S. (n=23 (tress- S!(9) 312 Sot 15(2) ISM (False) we cantake a large 3 (10) § Sinx ir aso then 7m >D lin ntot s(a)-110) a-o - Sin lin 2 tot lin (-1 - Sint) no = n2 tud orcole lin (x) (10) P (2) - 110) in oron oxi 22 ntor - lin Sinn-san aro xto ㅈ is is not differentiable atro false