Let g(x) = - for f(t) dt, where f is the function whose graph is shown. y f 0 1 3 6 (a) Use part one of the fundamental theorem of calculus to graph g'. What do you notice about the graphs? Og' is the inverse of f O g' is the same as f the magnitude of g' at the point (t, g'(t)) is the slope of f at the point (t, f(t)) O g' is equal to zero where f has a maximum and minimum the area under g' is greater than the area under f (b) Find g(3), g'(3), and g "(3). g(3) g'(3) 9"(3) (c) Does g have a local maximum, a local minimum, or neither at x = 6? O local maximum O local minimum O neither (d) Does g have a local maximum, a local minimum, or neither at x = 9? O local maximum local minimum O neither