The second derivative $\frac { d ^ { 2 } } { d x ^ { 2 } } \left( \left( x ^ { 2 } - 1 \right) ( x + 2 ) \right)$ is

A) $3 x ^ { 2 } + 4 x - 1$
B) $2 x$
C)0
D) $6 x + 4$
E) $6 x - 4$

Question

The second derivative $\frac { d ^ { 2 } } { d x ^ { 2 } } \left( \left( x ^ { 2 } - 1 \right) ( x + 2 ) \right)$ is

A) $3 x ^ { 2 } + 4 x - 1$
B) $2 x$
C)0
D) $6 x + 4$
E) $6 x - 4$

Quizplus · Accepted Answer

To find the second derivative, first, we need to expand and differentiate the given function twice. The function is $f(x) = (x^2 - 1)(x + 2)$. Expanding gives $f(x) = x^3 + 2x^2 - x - 2$. The first derivative is $f'(x) = 3x^2 + 4x - 1$, and the second derivative is $f''(x) = 6x + 4$.

The Second Derivative d2dx2((x2−1)(x+2))\frac { d ^ { 2 } } { d x ^ { 2 } } \left( \left( x ^ { 2 } - 1 \right) ( x + 2 ) \right)dx2d2​((x2−1)(x+2))

The Second Derivative $\frac { d ^ { 2 } } { d x ^ { 2 } } \left( \left( x ^ { 2 } - 1 \right) ( x + 2 ) \right)$