Question

how many relative extrema can the polynomial t(x) = 3x^2 - 5x + 8x^3 have? (1 point)

Explanation:

Step1: Identify the degree of the polynomial

The polynomial $t(x)=8x^{3}+3x^{2}-5x$ has degree $n = 3$.

Step2: Recall the rule for relative extrema

The number of relative extrema of a non - constant polynomial function is at most $n - 1$, where $n$ is the degree of the polynomial.
For a degree - 3 polynomial, the maximum number of relative extrema is $3-1=2$.

Answer:

2