How do you make a graph with polynomials with three hills?

Answer 1

To create a graph of a polynomial with three hills, you'll want a polynomial function that has three local maxima. A simple way to achieve this is to use a polynomial of degree 5 or higher, such as ( f(x) = x^5 - 15x^3 + 20x ), which has the necessary critical points. Use calculus to find the derivative, set it to zero, and solve for critical points to ensure there are three maxima. Finally, plot the function, ensuring it has the desired number of hills (peaks) between the x-intercepts.