Question

How many turns will the graph of f(x) = 3x5 -2x4 + 7x2 -9x + 8 have?

Answer 1

The number of turns of graph for
`f(x) = 3x^5 -2x^4 + 7x^2 -9x + 8` are 4

Explanation:

We need to find the number of turns the graph of
`f(x) = 3x^5 -2x^4 + 7x^2 -9x + 8` have?

Turns of graph:

The graphs turns when it changes from increasing to decreasing (rise to fall) or decreasing from increasing (fall to rise)

Turns of graph for a polynomial

A polynomial having degree n will have maximum n-1 turns.

So, for the given polynomial

`f(x) = 3x^5 -2x^4 + 7x^2 -9x + 8`

We need to find degree

The highest exponent of the polynomial is the degree of polynomial

So, Degree n = 5

Number of turns = n - 1 = 5-1 =4

So, the number of turns of graph for
`f(x) = 3x^5 -2x^4 + 7x^2 -9x + 8` are 4