Problem

f is a polynomial function of degree 42 :
The graph of f has at most x-intercepts.
The graph of f has at most turning points.

Answer

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Answer

Thus, the graph of f has at most 41 turning points.

Steps

Step 1 ：Let f be a polynomial function of degree 42.

Step 2 ：The number of x-intercepts of a polynomial function is determined by the degree of the polynomial. A polynomial of degree n can have at most n x-intercepts.

Step 3 ：Thus, the graph of f has at most 42 x-intercepts.

Step 4 ：The number of turning points of a polynomial function is also determined by the degree of the polynomial. A polynomial of degree n can have at most n-1 turning points.

Step 5 ：Thus, the graph of f has at most 41 turning points.

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