I have been stuck in this for a couple of hourscan someone h

I have been stuck in this for a couple of hours...can someone help? By looking at this graph, can you can you find the points of inflection? Here are my answers: y-intercepts are [0,1], these points are also the maxima. How do you find the t-intercepts? Thanks:)

Solution

The point of inflection are the points where the slope of the graph changes its sign i.e. becomes +ve from -ve or -ve from +ve. From the graph, y = 0.5 is the point of inflection. Hence t = 0, y = 0.5 is the point of inflection. t - intercepts are the points on the t-axis where the graph intersects the t-axis. Hence, t=2 and t=-2 are such points. Thus, the t-intercept is 2 units.