Sketch the Graph of a Continuous Function, If Possible, Such $f ^ { \prime }$

Essay

Sketch the graph of a continuous function, if possible, such that $f ^ { \prime }$ does not exist at $x = 0 , f ^ { \prime \prime } > 0$ on $( 0 , \infty )$ , $f ( x ) > 0$ on $( 1,5 ) , f ( x ) < 0$ on $( - \infty , 1 ]$ and on $[ 5 , \infty ) , f ^ { \prime } ( x ) > 0$ on $( - \infty , 3 ) , f ^ { \prime } < 0$ on $( 3 , \infty )$ , and $f ^ { \prime } ( x )$ does not exist at $x = 3$ .