IIT JAM Follow
February 8, 2022 12:44 am 30 pts
te Diferentiabi ability 17. Consider the function fC) =cos x+|sin(2- X)At which of the 21. The function f) =|xd+3 is following points is f not differentiable? (a.) Continuous as well as differentiable on R (a)(2n+1) ne z (b.) Continuous on R but not differentiable anywhere on R (c.) Continuous on Rand differentiable at all but finitely many points on R (b.) {nr:ne Z} (c.) {n + 2:ne Z} (d.) Non continuous on R 22. Let sx)=Isin Trl, xeR.Then a)ne (a.)fis continuous nowhere 18. For (b.) f is contínuous everywhere and n22, ley, : R >R S.(x) = x" sin x. Then at x = 0 S, has a be given by differentiable nowhere (c.) f is continuous everywhere differentiable everywhere except at integral value of (d.)f is differentiable everywhere and (a.) Local maximum if nis even (b.) Local maximum if n is odd (c.) Local minimum if n is even 23. The function f() =1-|1-x on R is (d.) Local minimum if n is odd (a.) Not continuous 19. Let f:R>R be defined by b.) Continuous but not differentiable (c.) Differentiable but not continuous fx)=r'sin,x+0, f0) =0 (d.) Differentiable at only one point f:[0, 1]>R is a function. Which of the following is possible? (a.) f is differentiable everywhere with 24. continuous derivative (a.) f is differentiable but not continuous (b.) fis differentiable everywhere other than the point 1 (b.) f is unbounded and continuous (c.) f is differentiable but its derivativeis (c.) f is nowhere differentiable not continuous (d.) f is differentiable but its derivative is (d.) f is continuous but not integrable not continuous 25. Let f=RR be differentiable. Which of 20. Define these will follow from mean value theoremn? From m, nE N (a.) For all a,b in R, if an (6.) Differentiable for each pair m,n with (a, b) such that /@- (tc b-a m
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