A team of researchers finds that there is a relationship between the overall health of a forest they're studying and the population of a certain beetle which feeds on the bark of old-growth trees. Due to the warming climate, the beetles are now able to reproduce one more time per year than they previously did, exacerbating the stress caused by the drought of the past few seasons. They use the function f (x) = 13x"+67 to model .6x5+39 the relationship between the two populations, where x is in tens of thousands of beetles and f is in thousands of trees. They note that there is a beneficial contribution to the ecosystem as a whole for a smaller population of the beetles, but that the number of healthy trees sharply declines as the beetle population rises too much. 1. Graph f (x) using technology. a. What appears to be the maximum number of healthy trees, to the nearest thousand? What is the estimated beetle population corresponding to this, to the nearest ten thousand? b. What is the slope of the tangent line to the graph of f (x) at the point corresponding to the maximum number of healthy trees (and the optimal population of beetles)? How do you know?