Problem 10

Given information

Function is continuous in the given domain , but is has no local maximum and no local minimum, and also and are critical points of a function. Critical points of a continuous function within it's domain is defined as the points where derivative of the function is zero or slope of the function is zero and the points where slope of function changes.  

Step-by-step explanation

As function is continuous within it's domain and it neither has local minimum nor local maximum therefore function must be either continuously increasing or continuously decreasing and also as no information regarding it's differentiability is given we will adopt simplest function to draw the graph of this function which is linearly variable function or a straight line. But the function have two critical points namely  and , therefore we will start from , adopt value of function at this point be  , as is a critical point therefore slope must change at this point so adopt value of function at this point be , also is a critical point therefore slope of the function will also change at this point, assume value of function at this point be . As the function has no local maximum and no local minimum therefore we will adopt the function to be continuously increasing function.