64
1.6. THE SECOND DERIVATIVE
4. For each prompt that follows, sketch a possible graph of a function on the interval
−3 < x < 3 that satisfies the stated properties.
(a) y = f (x) such that f is increasing on −3 < x < 3, f is concave up on
−3 < x < 0, and f is concave down on 0 < x < 3.
(b) y = g(x) such that g is increasing on −3 < x < 3, g is concave down on
−3 < x < 0, and g is concave up on 0 < x < 3.
(c) y = h(x) such that h is decreasing on −3 < x < 3, h is concave up on
−3 < x < −1, neither concave up nor concave down on −1 < x < 1, and h is
concave down on 1 < x < 3.
(d) y = p(x) such that p is decreasing and concave down on −3 < x < 0 and p is
increasing and concave down on 0 < x < 3.
1.6. THE SECOND DERIVATIVE
4. For each prompt that follows, sketch a possible graph of a function on the interval
−3 < x < 3 that satisfies the stated properties.
(a) y = f (x) such that f is increasing on −3 < x < 3, f is concave up on
−3 < x < 0, and f is concave down on 0 < x < 3.
(b) y = g(x) such that g is increasing on −3 < x < 3, g is concave down on
−3 < x < 0, and g is concave up on 0 < x < 3.
(c) y = h(x) such that h is decreasing on −3 < x < 3, h is concave up on
−3 < x < −1, neither concave up nor concave down on −1 < x < 1, and h is
concave down on 1 < x < 3.
(d) y = p(x) such that p is decreasing and concave down on −3 < x < 0 and p is
increasing and concave down on 0 < x < 3.