Let `f(x)` be a polynomial of degree 3 having a local maximum at `x=-1.` If `f(-1)=2,\ f(3)=18 ,` and `f^(prime)(x)` has a local minimum at `x=0,` then distance between `(-1,\ 2)a n d\ (a ,\ f(a)),` which are the points of local maximum and local minimum on the curve `y=f(x)` is `2sqrt(5)` `f(x)` is a decreasing function for `1lt=xlt=2sqrt(5)` `f^(prime)(x)` has a local maximum at `x=2sqrt(5)` `f(x)` has a local minimum at `x=1`