Let A(x) = x a (t) dt. Match the property of A with the corresponding property

Let A(x) = ∫^x_a ƒ(t) dt.

Match the property of A with the corresponding property of the graph of ƒ. Assume ƒ is differentiable.

Area function A
(a) A is decreasing.
(b) A has a local maximum.
(c) A is concave up.
(d) A goes from concave up to concave down.
Graph of ƒ
(i) Lies below the x-axis.
(ii) Crosses the x-axis from positive to negative.
(iii) Has a local maximum.
(iv) ƒ is increasing.