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sketch or show that it is impossible to sketch the graph of function f(x) such that: f'(3)=0 f'(x)positive for all f(x) bigger than 0 for x in:

sketch or show that it is impossible to sketch the graph of function f(x) such that:

f'(3)=0
f'(x)positive for all f(x) bigger than 0 for x in:
(- infinity, 1), (3,4) and (4,infinity)
f'(x) negative for all f(x) smaller than 0 for x in (1,3)

f(-3)= f(5)= 0
f"(x) negative for all f"(x) smallar than 0 for x in:
(- infinity,-2) and (4,infinity)
f"(x) positive for all f"(x) bigger than 0 for x in:
(-2,1) and (1,4)
f(0)= f(3)= 2
lim ((x goes to - infinity )) f(x)= - infinity
lim (( x goes to infinity )) f(x)= 7

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