Problem

Problem

If

f(x)

is a cubic polynomial which has local maximum at

x = -1

. If

f(2) = 18

,

f(1) = -1

and

f'(x)

has local minimum at

x = 0

, then a. the distance between

(-1, 2)

and

(a, f(a))

, where

x = a

is the point of local minima, is

2\sqrt{5}

b.

f(x)

is increasing for

x \in [1, 2\sqrt{5}]

c.

f(x)

has local minima at

x = 1

d. the value of

f(0) = 5

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