Answer:
The number of turns of graph for [tex]f(x) = 3x^5 -2x^4 + 7x^2 -9x + 8[/tex] are 4
Step-by-step explanation:
We need to find the number of turns the graph of [tex]f(x) = 3x^5 -2x^4 + 7x^2 -9x + 8[/tex] 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
[tex]f(x) = 3x^5 -2x^4 + 7x^2 -9x + 8[/tex]
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 [tex]f(x) = 3x^5 -2x^4 + 7x^2 -9x + 8[/tex] are 4
