Question

Below is the graph of a polynomial function with real coefficients

Answer 1

Part (a)

The function is decreasing when the graph is going down.

So, the answer is
`(-8, -6), (-2, 3), (7, 9)`.

Part (b)

Local minima are where the function changes from decreasing to increasing.

So, the answer is
`-6, 3, 9`.

Part (c)

Since the sum of the multiplicities of the roots is
`1+1+2=4`, this means that since
`y \to \infty` as
`x \to \infty`, the leading coefficient is positive.