Part 4 of 7 112 points Answer parts (a)-(e) for the function shown below \[ f(x)=x^{3}-2 x^{2}-x+2 \] At which \( x \)-intercept(s) does the graph cross the \( x \)-axis? Select the correct choice below and, if necessary, fill in the answer box to complete your choice A. \[ x=-1,1,2 \] (Type an integer or a decimal. Use a comma to separate answers as needed.) B. There are no \( x \)-intercepts at which the graph crosses the x -axis. At which x -intercept(s) does the graph touch the x -axis and turn around? Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. \( x= \) \( \square \) (Type an integer or a decimal. Use a comma to separate answers as needed ) B. There are no \( x \)-intercepts at which the graph touches the \( x \)-axis and turns around

To determine the \( x \)-intercepts where the graph of the function \( f(x)=x^{3}-2 x^{2}-x+2 \) crosses the \( x \)-axis, we need to find the roots of the equation \( f(x) = 0 \). After evaluating the polynomial, we find the roots to be \( x = -1, 1, \) and \( 2 \). Since the function has alternating behavior on these roots, the graph crosses the \( x \)-axis at all of these points. So, the answer for the points where the graph crosses the \( x \)-axis is: A. \[ x=-1,1,2 \] For determining at which \( x \)-intercept the graph touches the \( x \)-axis and turns around, we can check the derivatives or the behavior of \( f(x) \) near its roots. It turns out to be that at \( x = 1 \), the function's derivative indicates a local maximum, suggesting the graph touches and turns around at this point. So, the answer for the point where the graph touches the \( x \)-axis and turns around is: A. \( x=1 \)