Suppose we have a function g with domain (-,) is continuous and differentiable everywhere and with g'(52)=0.For each scenario below, decide if we can conclude that g(x) has a local minimum at x=52 from the information. If yes, write yes and explain briefly. If we cannot conclude this, explain why not briefly. (Words or picture can be used to explain why.)(a)g'(x)<0 for x<52 and g'(x)>0 for x>52(b)g'(x)>0 for x<52 and g'(x)<0 for x>52(c)g''(x)<0 for x<52 and g''(x)>0 for x>52(d)g''(52)<0(e)g''(52)>0(f)g(52)=0,g(2)=1, and g(3)=1.Modified from Gottlieb, Rates of Change.