Question

True or False Basic Differential Equations?

Answer 1

Suppose that y = f(x) is a solution of the differential equation \[\frac{ dy }{dx } = g(x) \]
Determine if the following are true or false.

(a) If g(x) is increasing for all x, then the graph of f is concave up for all x.

(b) If g(0) = 1 and g(x) is increasing for x ≥ 0, then f(x) is also increasing for x ≥ 0.

(c) If lim x→∞ g(x) = 0 then lim x→∞ f(x) = 0
.
(d) If g(x) is even, then so is f(x).