The polynomial function \( g \) is defined by \( g(x)=4 x^{4}+2 x^{3}-8 x^{2}-5 x+2 \). Use the ALEKS graphing calculator to find all the points \( (x, g(x)) \) where there is a local maximum.

To find the points where the polynomial function \( g(x) = 4x^4 + 2x^3 - 8x^2 - 5x + 2 \) has local maxima, you can start by finding its critical points. This involves taking the derivative of \( g(x) \) and setting it equal to zero. The derivative is \( g'(x) = 16x^3 + 6x^2 - 16x - 5 \). After finding the critical points by solving \( g'(x) = 0 \), you can then use the second derivative test or the first derivative test to determine which points are local maxima. Once you have the critical points, you should evaluate \( g(x) \) at these points to find the corresponding \( g(x) \) values. The local maximum points will be of the form \( (x, g(x)) \). Don't forget to also check the behavior of \( g'(x) \) around these critical points to confirm they are indeed local maxima! You might want to graph the function or use the graphing calculator on ALEKS to visualize where those maxima are located. Happy graphing!