Consider the following. f ( x ) = 3 + 3 x - x 3 (a) Find the interval(s) of incr
ID: 2870416 • Letter: C
Question
Consider the following.
f(x) = 3 + 3x - x3
(a) Find the interval(s) of increase. (Select all that apply.)
(-, -1)(-, 0)(-2, 0)(0, 2)(-1, 1)(1, )(0, )(-, )none of these
Find the interval(s) of decrease (Select all that apply.)
(-, -1)(-, 0)(-1, 0)(0, 1)(-1, 1)(1, )(0, )(-, )none of these
(b) Find the local maximum value(s). (Select all that apply.)
--11425none of these
Find the local minimum value(s). (Select all that apply.)
--11425none of these
(c) On what interval(s) is f concave upward? (Select all that apply.)
(-, 0)(0, 2)(0, 1)(-1, 1)(1, )(0, )(-, )none of these
On what interval(s) is f concave downward? (Select all that apply.)
(-, -1)(-, 0)(-1, 0)(-2, 1)(-1, 1)(0, )(-, )none of these
What are the inflection point(s) of f ? (Select all that apply.)
(-1, 0)(0, 3)(1, 4)(2, 0)none of these
Explanation / Answer
f(x) = 3 + 3x - x^3
f'(x)=3-3x^2 ,f"(x)=-6x
(a) Find the interval(s) of increase. f'(x)=3-3x^2>0 ==>(1-x^2)>0==>(1-x)*(1+x)>0==>(x-1)*(x+1)<0
x= (-1, 1)
Find the interval(s) of decrease f'(x)=3-3x^2<0 ==>(1-x^2)<0==>(1-x)*(1+x)<0==>(x-1)*(x+1)>0
x= (-, -1)u(1, )
(b) Find the local maximum value(s). (Select all that apply.)
f(1)=3+3-1 =5
Find the local minimum value(s). (Select all that apply.)
f(-1)=3-3+1 =1
(c) On what interval(s) is f concave upward? (Select all that apply.)
f"(x)>0==>-6x>0 ==>6x<0
(-, 0)
On what interval(s) is f concave downward? (Select all that apply.)
f"(x)<0 ==>-6x<0==>6x>0
(0, )
What are the inflection point(s) of f ? (Select all that apply.)
f"(x)=0
==>-6x=0
x=0
(x,f(x))=(0,f(0)) =(0,3)