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
From the possible graph of \( y=f(x) \), we can say that
(a) there is exactly one point of inflection on the curve
(b) \( f(x) \) increases on \( -5x2 \) and \( x4 \) and decreases on \( -\inftyx-5 \) and \( 2x4 \)
(c) the curve is always concave down
(d) curve always concave up
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