Question

For \[f(x)=3x^4+4x^3-12x^2+12\], what conclusion follows at \[x=-2\]?

Options

• Local minimum value \[=-20\] at \[x=-2\]

• Local maximum value \[=-20\] at \[x=-2\]

• point of inflection at \[x=-2\]

• Local minimum value \[=7\] at \[x=-2\]

Answer 1

Since \[f''(-2)=72>0\], \[x=-2\] is a point of local minimum. Evaluating the function gives \[f(-2)=48-32-48+12=-20\].