SOLUTION: for the function f(x), find the maximum number of real zeros,the maximm number of x-intercepts, and the maximum number of turning points that the function can f(x)=x^6-x^3+3

Question 1050020: for the function f(x), find the maximum number of real zeros,the maximm number of x-intercepts, and the maximum number of turning points that the function can f(x)=x^6-x^3+3
Found 2 solutions by josgarithmetic, ikleyn:
Answer by josgarithmetic(39617) (Show Source): You can put this solution on YOUR website!
Know the basic shapes for polynomial functions.

Degree 6 means maximum six possible x-intercepts;
Lead coefficient is positive, so left and right sides go upward, and three possible valleys and two possible humps;

Can you factorize your f(x) ?
Is it in quadratic form? Not a question of if it is or is not quadratic, but "FORM".
Is it symmetric around a vertical axis (like, is f(x) an even function)?

Checking with graphing feature of google search engine, your f seems symmetric around x=0 but seems to have NO real zeros. Very very very flat between x=5 and x=-5.
Answer by ikleyn(52777) (Show Source): You can put this solution on YOUR website!
.

Plot y =

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