(4 marks) Consider a function

f

with

f^(')(0)=f^(')(1)=0

. Suppose that

f^('')(0)>0

while

f^('')(1)=0

.\ Which of the following statements could be correct?\ Fill in all the correct options for this question.\ 0 is a local minimum of

f

and 1 is a local minimum of

f

\ 0 is a local minimum of

f

and 1 is a local maximum of

f

\ 0 is a local maximum of

f

and 1 is a local minimum of

f

\ 0 is a local maximum of

f

and 1 is a local maximum of

f

7. (4 marks) Consider a function f with f(0)=f(1)=0. Suppose that f(0)>0 while f(1)=0. Which of the following statements could be correct? Fill in all the correct options for this question. 0 is a local minimum of f and 1 is a local minimum of f 0 is a local minimum of f and 1 is a local maximum of f 0 is a local maximum of f and 1 is a local minimum of f 0 is a local maximum of f and 1 is a local maximum of f