If is a cubic polynomial which has a local maximum at , ,

MATHEMATICS · Multi correct · AP · Calculus AB · Analytical Applications of Differentiation · Analytical Applications of Differentiation

Problem

f(x)

is a cubic polynomial which has a local maximum at

x=-1

f(2)=18

f(1)=-1

, and

f'(x)

has a local minimum at

x=0

, then (1) The distance between

(-1,2)

and

(a,f(a))

, where

x=a

is the point of local minimum, is

2\sqrt{5}

. (2)

f(x)

is increasing for

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

. (3)

f(x)

has a local minimum at

x=1

. (4)

f(0)=5