Let g(x) = / f(t) dt, where f is the function whose graph is shown. 9 6 3 3 6 9 2 15 18 21 - 3 (a) Evaluate g(x) for x = 0, 3, 6, 9, 12, 15, and 18. 9(0) = 9 (3 ) = 9(6) = 9(9) = g(12) : 9(15) = g(18) = (b) Estimate g(21). (Use the midpoint to get the most precise estimate.) g(21) = (c) Where does g have a maximum value? Where does it have a minimum value? minimum X = maximum\fLet g(x) = "(t) dt, where f is the function whose graph is shown. f 0 3 6 9 (a) Use part one of the fundamental theorem of calculus to graph g'. What do you notice about the graphs? O 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 O g' is the inverse of f O g' is the same as f the area under g' is greater than the area under f (b) Find g(3), g'(3), and g "(3). 9 (3 ) 9 (3 ) g " (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 O local minimum neither