- The graph of f is a polynomial function
- There are two turning points, namely, x = 0 and x = -2
Explanation:
A polynomial function in one variable is given by the form:
[tex]f(x)=a_{n}x^n+a_{n-1}x^{n-1}+\cdots +a_{2}x^2+a_{1}x+a_{0}[/tex]
Since you haven't provided any expression, I'll choose the following function:
[tex]f(x)=x^{3}+3x^{2}+3[/tex]
So this is indeed a polynomial function. A turning point is an x-value where we have either a local maximum or local minimum. So we need to take the derivative of this functions:
[tex]f'(x)=3x^2+6x \\ \\ Finding \ turning \ points: \\ \\ 3x^2+6x=0 \\ \\ x(3x+6)=0 \\ \\ \\ So: \\ \\ x=0 \\ \\ and \\ \\ \ 3x+6=0 \therefore \ \boxed{x=-2}[/tex]
Conclusion:
- The graph of f is a polynomial function
- There are two turning points, namely, x = 0 and x = -2
Learn more:
Polynomial function: https://brainly.com/question/13729121
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