(Solved): (1 point) Suppose that \[ f(x)=(x+6)(x-4)^{2} \] Our goal is to find the critical values of \( f \) ...

(1 point) Suppose that \[ f(x)=(x+6)(x-4)^{2} \] Our goal is to find the critical values of \( f \) and identify them as local maximums, local minimums, or neither. First find the derivative and second derivative: \[ \begin{array}{l} f^{\prime}(x)= \\ f^{\prime \prime}(x)= \end{array} \] (we recommend simplitying as much as possible) Next find all critical values of \( f \), If there are no critical values, entor - 1000 . If there are more than one, onter them soparated by oommas (f giving docimal values, give at least four digits after the decimal). Critical valuo(s) = Now use the second derivative test to find the \( x \)-coordinates of all local maxima of \( f \). If there are no local maxima, enter - 1000 . If there are more than one, enter them separated by commas. Local maxima at \( x= \) Use the second derivative test to find the \( x \)-coordinates of all local minima of \( f \). If there are no local minima, enter - 1000 . If there are more than one, enter thern separated by commas. Local minima at \( x= \)