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f(X)=(1-x)*(2-x) for 1 f(x)=(3-x) for x>2 ; Find whether x is differentiable at x=2 ; By { f(x+h)-f(x) }/h as h tends to zero method ,left hand derivate is 1 and right hand derivative is infinite; so at x=2 it is not differentiable by differentiation method ,i got right hand derivative=-1 , but using above method i got infinite.but Right hand limit by both the methods must be same ..Can anyone tell me why is this so ??
f(X)=(1-x)*(2-x) for  1f(x)=(3-x)  for  x>2 ; Find whether x is differentiable at x=2 ; By { f(x+h)-f(x) }/h  as h tends to zero  method ,left hand derivate is  1  and right hand derivative is infinite; so at x=2 it is not differentiable by differentiation method ,i got right hand derivative=-1 , but using above method i got infinite.but Right hand limit by both the methods must be same ..Can anyone tell me why is this so ??


one year ago

2075 Points
							hello praveen, lets use the { f(x+h)-f(x) }/h method for right hand limit. we wish to find lim h tends to 0+ { f(2+h)-f(2) }/hnow, you have typed the question incompletely. so i dont know what f(2) is. actually, its not ur fault it is askiitians websites fault that when u try to type inequality signs, they often mess up.so, kindly reupload the ques with a pic.btw, it doesnt matter what the actual ques is. the fact is that f(x) is not differentiable at x=2. the reason is that f(x) is not continuous at x=2.we see that lim x tends to 2- f(x)= lim x tends to 2- (1-x)*(2-x) = 0while lim x tends to 2+ f(x)= lim x tends to 2+ (3-x) = 1so, no matter what the value of f(2) is, f(x) can never be differentiable at 2 since it is not continuous there in the first place.kindly approve yar :=)

one year ago
Vikas TU
14148 Points
							Dear student we see that lim x tends to 2- f(x)= lim x tends to 2- (1-x)*(2-x) = 0while lim x tends to 2+ f(x)= lim x tends to 2+ (3-x) = 1obviously RHL does not equal LHL. so it is not continuous.recall the theorem that if f(x) is not continuous at x=a, it cannot be differentiable too at x=a.so f(x) is not differentiable at 2 since it is not continuous at x= 2 in the first place.

one year ago
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