Use a graphing calculator to estimate the local maximum and local minimum values of the function to the nearest
hundredth.
-The following polynomial approximates the rabbit population in a particular area, R(x) = -0.135x5 + 2.952x4 + 3500, where x is the number of years from 1995. Use a graphing calculator to
Describe the rabbit population from the years 1995 to 2010.
A) The population decreases.
B) The population remains stable.
C) The population increases.

Question

Quizplus · Accepted Answer

Given the polynomial R(x) = -0.135x^5 + 2.952x^4 + 3500, where x represents the years from 1995, to analyze the rabbit population from 1995 to 2010, we substitute the range of x from 0 to 15 into the equation. The negative coefficient of the highest power term (-0.135x^5) suggests that the function eventually decreases for large values of x, but the presence of a positive x^4 term (2.952x^4) indicates that there might be an initial increase before any decrease. Without the exact graph, we rely on the general behavior of polynomials for interpretation. Since the question asks about the trend from 1995 to 2010 (a relatively short period in terms of polynomial behavior), and given the significant positive coefficient of the x^4 term, it's reasonable to infer that the population increases during this period before any long-term decline implied by the highest degree term.

Use a Graphing Calculator to Estimate the Local Maximum and Local