11.C
Take f(x)=a^{kx} & solve by substituting the given data....
1) Let f(x+y)= f(x).f(y) for all x & y. Given that f(3)=3 & f'(0)= 11.Then f'(3)= ?
A) 22 B) 44 C) 33 D) None
Assertion-Reason Type -
2) I- The sum or difference of two discontinuos functions may be continuous at a point.
II- If f(x) is continuous & g(x) is discontinuous at x=a, then f(x)±g(x) is discontinuous at x=a.
3) I- If the maximum value of y=lf(x)l exists in the interval (a,b), then it exists at critical point of y=f(x).
II- The critical points of y=lf(x)l are also critcal point of y=f(x).
A)-Both correct, II explains I.
B)-Both correct, II dosen't explain I.
C)-I correct; II wrong.
D)-I wrong; II correct.
E)- Both wrong
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13 Answers
106Q2. (b)
consider f(x) = [x] and g(x) = {x}
clearly f(x) + g(x) = x which is continuous
supports stmnt 1
Let g(a) ≠Lim(x→a) g(x) = h (the limit=h)
Lt(x→a) f(x)+g(x) = f(a)+h
But f(a)+g(a) ≠f(a)+h as g(a)≠h
So stmnt II is also true
1g(x)=[f(x)+g(x)] - f(x)
nw clearly we know difference of 2 continuous fn is continuous.... bt it is a contradiction 2 g(x)...hence stmnt II is true..
132) Yes, both are correct....agreed.
Me too did B), but answer is A).
How is II explaining I....?
106Q3. stmnt 1 is correct.. in open interval (a,b) we dont consider f(a) and f(b) for seeing the max or min.. hence if a max or min exists then it is at a critical point only.
obviously stmnt 2 is incorrect... as the critical pts obtained for lf(x)l x<0 will not be present for y=f(x)