and y-axes.
(b) Find the area of R.Part B. Directions: Answer these questions wtihout using your calculator.
- Draw a graph of y = f (x), given that f satisfies all the following conditions:
(1) f ′(−1) = f ′(1) = 0.
(2) If x < −1, f ′(x) > 0 but f ′′ < 0.
(3) If −1 < x < 0, f ′(x) > 0 and f ′′ > 0.
(4) If 0 < x < 1, f ′(x) > 0 but f ′′ < 0.
(5) If x > 1, f ′(x) < 0 and f ′′ < 0. - The figure below shows the graph of f ′, the derivative of f, with domain −3 ≤ x ≤ 9. The graph
of f ′ has horizontal tangents at x = 2 and x = 4, and a corner at x = 6.
(a) Is f continuous? Explain.
(b) Find all values of x at which f attains a relative minimum. Justify.
(c) Find all values of x at which f attains a relative maximum. Justify.
(d) At what value of x does f attain its absolute maximum? Justify.
(e) Find all values of x at which the graph of f has a point of inflection. Justify.- Find the area of the largest rectangle (with sides parallel to the coordinate axes) that can be
inscribed in the region bounded by the graphs of f (x) = 8 − 2x^2 and g(x) = x^2 − 4. - Given the graph of f (x), sketch the graph of f ′(x).