Question

1. f(x) = x³ - 2x² + 4

Explanation:

Step1: Recall the rule for turning points

The maximum number of turning points of a polynomial function \( f(x) \) of degree \( n \) is \( n - 1 \).

Step2: Determine the degree of the polynomial

For the function \( f(x)=x^{3}-2x^{2}+4 \), the highest power of \( x \) is 3, so the degree \( n = 3 \).

Step3: Calculate the maximum number of turning points

Using the formula \( n - 1 \), substitute \( n = 3 \): \( 3-1 = 2 \).

Answer:

The maximum number of turning points of the graph of \( f(x)=x^{3}-2x^{2}+4 \) is \( 2 \).