f(x)=−4+x6−x3−3x−3x2−2x4−2x5 Based on the degree of the polynomial f(x) given below, what is the maximum...

Maria Huey

Maria Huey

Answered

2022-01-17

f(x)=4+x6x33x3x22x42x5
Based on the degree of the polynomial f(x) given below, what is the maximum number of turning points the graph of f(x) can have?

Answer & Explanation

Ben Owens

Ben Owens

Expert

2022-01-18Added 27 answers

Step 1
Turning Point: A turning point is a point of the graph where the graphchanges from increasing to decreasing or decreasing to increasing
Step 2
Note : A polynomial of degree n will have as most (n−1) turning points
f(x)=4+x6x33x3x22x42x5
=2x42x5
degree (f(x))=6
f(x) can have 6-1 = 5 turning points i.e ,maximum number of turning points is 5

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