Question

For \[f(x)=3x^4+4x^3-12x^2+12\], what conclusion follows at \[x=1\]?

Options

• Local minimum value \[=-20\] at \[x=1\]

• Local maximum value \[=12\] at \[x=1\]

• Local minimum value \[=7\] at \[x=1\]

• Local maximum value \[=7\] at \[x=1\]

Answer 1

Since \[f''(1)=36>0\], \[x=1\] is a point of local minimum. Substitution gives \[f(1)=3+4-12+12=7\].