Suppose you do not know the function \( f(x) \), however some information about \( f(x) \) is li...

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Suppose you do not know the function \( f(x) \), however some information about \( f(x) \) is listed below.
Read the following carefully before attempting the questions
(i) \( f(x) \) is continuous and defined for all real numbers
(ii) \( f^{\prime}(-5)=0, f^{\prime}(2) \) is not defined and \( f^{\prime}(4)=0 \)
(iii) \( (-5,12) \) is a point which lies on the graph of \( f(x) \)
(iv) \( f^{\prime \prime}(2) \) is undefined, but \( f^{\prime \prime}(x) \) is negative everywhere else
(v) The signs of \( f^{\prime}(x) \) is given below
On the possible graph of \( y=f(x) \), we have
(a) \( x=-5 \) is a point of relative minima
(b) \( x=2 \) is a point of relative maxima
(c) \( x=4 \) is a point of relative minima
(d) graph of \( y=f(x) \) must have a geometrically sharp corner
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