(a)True/False. Letf(x) be a function with f′(a) = 0,f′′(a) = 0, and f′′′(a) = 0f or some real number a. Then f(x) = c for some real number c.

(b)True/False. Let f(x) and g(x) be two functions. Assume that for some real number a both of the equalities f(a) =g(a) and f′′(a) =g′′(a) are true. Then it follows that f′(a) = g′(a).

(c)Explain. Graph the function f(x) = x^2+1/x−2. Label all relative minima, relative maxima, and inflection points. (Hint: there is a vertical asymptote at x= 0 so the graph is in two pieces).

(d)Solve. Compute f′′(1) where f(x) = ln(x)·(xe^x^2).