[tex]\begin{gathered} f(x)=x^3+3x^2-x-24 \\ f^{\prime}(x)=3x^2+6x-1 \\ f^{\doubleprime}(x)=6x+6 \\ So,\text{ }6x+6=0 \\ x=-1 \\ So,\text{ at x=-1 in the f(x)} \\ f(x)=(-1)^3+3(-1)^2-(-1)-24 \\ f(x)=-1+3+1-24 \\ f(x)=-21 \\ So,\text{ inflectio point (-1,-21)} \end{gathered}[/tex]
