The differential equation has a slope field in which every segment tilts upward and…
MATHEMATICS · Single correct · AP · Calculus AB · Differential Equations · Differential Equations
Problem
The differential equation dxdy=x2+1 has a slope field in which every segment tilts upward and becomes steeper as ∣x∣ increases. Which statement best describes any solution curve to this differential equation?
(a) The solution decreases for x<0 and increases for x>0 because the slopes are negative on the left of the y-axis and positive on the right.
(b) The solution increases for all real x but becomes flatter as ∣x∣ grows because the slopes approach zero.
(c) The solution increases for all real x and becomes steeper as ∣x∣ grows.
(d) The solution has a horizontal tangent at x=0 because the slope there is zero.