Suppose you do not know the function $f(x)$, however some information about $f(x)$ is listed below.

Question

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

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