(Solved): 21 Consider the function \( f(x)=2 x^{3}-6 x^{2}-18 x+54 \). Answer the questions below. If you h ...

21

Consider the function \( f(x)=2 x^{3}-6 x^{2}-18 x+54 \). Answer the questions below. If you have to enter more than one number or interval, separate your answers with commas. Find the first derivative. \( f^{\prime}(x)= \) List any critical values. Identify intervals of increase. Identify intervals of decrease. Find the second derivaitve. \( f^{\prime \prime}(x)= \) Use the information above to identify maximums as points. Use the information above to identify minimums as points. Use the second derivative to identify intervals where \( f(x) \) is concave up. Use the second derivative to identify intervals where \( f(x) \) is concave down. Use the second derivative to find any inflection points.