# "From what I understand, you want to know about the" #

# "downward concavity of the graph of the function." #

# "(Please correct me if I am wrong !!)" #

# "To investigate the concavity of a function, we will look" #

# "at" \ \ f''(x)." #

# "We are given the function:" #

# \qquad \qquad \qquad \qquad \qquad \qquad \qquad \qquad \qquad f(x) \ = \ 2 - 7 x^4. #

# "We compute derivatives:" #

# \qquad \qquad \qquad \qquad \qquad \qquad \qquad \qquad \qquad f'(x) \ = \ 0 - 7 ( 4 x^3) #

# \qquad \qquad \qquad \qquad \qquad \qquad \qquad \qquad \qquad f'(x) \ = \ - 28 x^3. #

# \qquad \qquad :. \qquad \qquad \qquad \qquad \quad \quad \ f''(x) \ = \ - 28 ( 3 x^2 ). #

# \qquad \qquad \qquad \qquad \qquad \qquad \qquad \quad \quad \ \ f''(x) \ = \ - 84 x^2. #

# "Perhaps before anything else, we note that" \ \ f''(x) \ \ "is clearly" #

# "negative everywhere:" #

# \qquad \qquad \qquad \qquad \qquad \qquad \qquad \qquad \ f''(x) \ < \ 0, \qquad \qquad \qquad \qquad "for all" \ \ x. #

# "Thus, the graph of" \ \ f(x) \ \ "is concave down everywhere:" #

# \qquad \qquad "the graph of" \ \ f(x) \ \ "is concave down on" \ \ ( -infty, infty)." #