Question

Sketch the graph of a function that satisfies all of the given conditions.
f'(x)>0 if |x|<2
f'(x)<0 if |x|>2
f'(2)=0
limit as x->infinity f(x)=1
f(-x)=-f(x)
f"(x)<0 if 00 if x>3 I can't put them all together. help pleasee

Answer 1

You have to concern for x>0

Answer 2

and for x<0 it should be odd function.

Answer 3

So x>2 f'<0 and x<2 f'>0 and f'2=0 -> f is max in x=2

Answer 4

then it is min in x=-2

Answer 5

limf x->inf is 1
so limf when x->-inf is -1

Answer 6

i just dont know how to put the graph together