Use a graphing calculator to estimate the local maximum and local minimum values of the function to the nearest
hundredth.
-The polynomial $R ( x ) = - 0.021 x ^ { 5 } + 4.133 x ^ { 4 } + 300$ approximates the shark population in a particular area, where x is the number of years from 1985. Use a graphing calculator to describe the shark population from the years
1985 to 2010.
A) The population decreases.
B) The population increases.
C) The population remains stable.

Question

Quizplus · Accepted Answer

Given the polynomial $R(x) = -0.021x^5 + 4.133x^4 + 300$, when graphed for the years from 1985 to 2010 (which translates to $x$ values from 0 to 25), the general trend shows an increase in the shark population. This is because the positive quartic term ($4.133x^4$) dominates the negative quintic term ($-0.021x^5$) in this range, leading to an overall increase in $R(x)$, which represents the shark population.

Use a Graphing Calculator to Estimate the Local Maximum and Local