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The function `f(x)={ 1-2x+3x^2-4x^3; x!=-1, 1; x=-1}`discuss the continuity and differentiablilty at `x=-1`.A. continuous and derivable at `x=-1`B. Neither continuous nor derivable at `x=-1`C. Continuous but not derivasble at `x=-1`D. continuous but not derivable at `x=0` |
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Answer» Correct Answer - B For `x!=-1` `f(x)=1-2x+3x^(2)-4x^(3)+……….prop` `f(x)k=(1+x)^(-2)=1/((1+x)^(2))` LHL`=lim_(hrarr0)f(-1-h)=lim_(hrarr0)1/((1-1-h)^(2))rarroo` `impliesf(x)` is not continuous at `x=-1` so,`f(x)` is not derivative at `x=-1` hecne `f(x)` is neither continuous nor derivable at `x=-1` |
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