This problem illustrates the Second Derivative Test.Let f(x)=arctan(x2)+6.(a) Find f'(x) = (b) Find the critical point of f(x).x = (c) Find f''(x) = (d) Use the Second Derivative Test to classify the critical point of f.f''(c.p.) = .This means that f is ---Select---concave upconcave down at the critical point becausef''(c.p.) is ---Select---positivenegative .We conclude that the critical point is ---Select---a local maximuma local minimum of f.