Final answer:
To graph the polynomial P(x) = 3x⁴ - 4x³ - 10x - 1, use a graphing device or software and find the x-intercepts, y-intercept, local extrema, and end behavior of the polynomial.
Step-by-step explanation:
To graph the polynomial P(x) = 3x⁴ - 4x³ - 10x - 1, we can use a graphing device or software such as Desmos or GeoGebra. By inputting the equation into the graphing device, we can obtain the graph.
The x-intercepts are the points where the graph intersects the x-axis. To find the x-intercepts, we set P(x) = 0 and solve for x. The y-intercept is the point where the graph intersects the y-axis; to find it, we set x = 0 and evaluate P(x).
The local extrema are the points on the graph where the slope changes from positive to negative or vice versa. We can find them by analyzing the critical points of the polynomial, which occur where the derivative of P(x) equals zero. Finally, the end behavior of the polynomial can be determined by examining the leading term of the polynomial, which is the term with the highest degree.