JEE Advance - Mathematics (2006 - No. 29)
$$f(x)$$ is cubic polynomial with $$f(2)=18$$ and $$f(1)=-1$$. Also $$f(x)$$ has local maxima at $$x=-1$$ and $$f'(x)$$ has local minima at $$x=0$$, then
the distance between $$(-1,2)$$ and (a$$f(a)$$) where $$x=a$$ is the point of local minima is $$2\sqrt 5 $$
$$f(x)$$ is increasing for $$x \in \left[ {1,2\sqrt 5 } \right]$$
$$f(x)$$ has local minima at $$x=1$$
the value of $$f(0)=15$$