(Solved): Consider the following function. f(x)=x33x26x+5 Find the first and second derivatives. f(x ...

Consider the following function. $f(x)=x^3-3x^2-6x+5$ Find the first and second derivatives. $f^{\prime }(x)=$ $f^{\prime \prime }(x)=$ Find any values of $c$ such that $f^{\prime \prime }(c)=0$. (Enter your answer as a comma-separated list. If any answer does not exist, enter DNE) $c=$ Find the interval(s) on which $f$ is concave up. (Enter your answer using interval notation.) Find the interval(s) on which $f$ is concave down. (Enter your answer using interval notation.) Find the inflection point of $f$. $(x,y)=\left((1,-3){}_x\right)$