Question

Find the points of inflection. f(x) = x3 + 3x2 - X - 24 O (-1,3) 0 (-1,0) O (1,8) 0 (-1, -21)

Answer 1

`\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}`