The function `f(x)={ 1-2x+3x^2-4x^3; x!=-1, 1; x=-1}` discuss the continuity and differentiablilty at `x=-1`.

Options

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`

Answer

B

Explanation

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`