For the function fx find the maximum number of real zeros th

For the function f(x), find the maximum number of real zeros, the maximum number of x-intercepts, and the maximum number of turning points that the function can have.

f(x) = -6x - x⁴

Solution

Since the function is degree 4, it has exactly 4 zeros. It has a maximum of 4 real zeros. The function will have an x-intercept corresponding to every real zero, so it has a maximum of 4 x-intercepts. A polynomial function of degree n has at most n - 1 turning points, so 4 - 1 = 3 turning points, maximum