# Video: Identifying the Concavity and Monotonicity of a Function from Its Graph

Consider the given slope field graph representing a differential equation. If the solution of the differential equation contains point π, which point can also belong to the solution?

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### Video Transcript

Consider the given slope field graph representing a differential equation. If the solution of the differential equation contains point π, which point can also belong to the solution?

Letβs trace solution curves through each of the points in the direction of the pattern of slopes mapped out through the line segments. Starting at the point in question, π, we can see that the solution curve could go through the point πΆ. Although πΆ doesnβt lie exactly on the line segment, it is within the pattern of the slope field marked out by a solution through the point π. So point πΆ is a contender for the solution through π. Letβs also check the points π΄, π΅, π·, and πΈ. Following the pattern of the slope field through the point π΄, the solution does not coincide with the point π. So the point π΄ cannot belong to the same solution as π. Following the pattern through the point π΅, again this solution does not coincide with the point π. The same applies for point π· and also for point πΈ, so that only point πΆ could belong to a solution containing the point π.