Second Derivative Test

1. Find the first derivative of the function $\displaystyle {g{{\left({x}\right)}}}={6}{x}^{{3}}+{18}{x}^{{2}}-{54}{x}$.
   $\displaystyle {g}'{\left({x}\right)}=$Preview Question 6 Part 1 of 5  
   
   
2. Find the second derivative of the function.
   g"$\displaystyle {\left({x}\right)}=$Preview Question 6 Part 2 of 5  
   
   
3. Evaluate g"$\displaystyle {\left(-{3}\right)}$.
   g"$\displaystyle {\left(-{3}\right)}=$
   
   
4. Is the graph of $\displaystyle {g{{\left({x}\right)}}}$ concave up or concave down at $\displaystyle {x}=-{3}$?
   At $\displaystyle {x}=-{3}$ the graph of $\displaystyle {g{{\left({x}\right)}}}$ is concave
   
   
5. Does the graph of $\displaystyle {g{{\left({x}\right)}}}$ have a local minimum or local maximum at $\displaystyle {x}=-{3}$?
   At $\displaystyle {x}=-{3}$ there is a local