Question

For \[f(x)=3x^4+4x^3-12x^2+12\], what conclusion follows at \[x=0\]?

Options

• Local minimum value \[=12\] at \[x=0\]

• Local maximum value \[=12\] at \[x=0\]

• Local minimum value \[=7\] at \[x=0\]

• point of inflection at \[x=0\]

Answer 1

Here \[f''(0)=-24<0\], so \[x=0\] is a point of local maximum. Also, \[f(0)=12\], giving local maximum value \[12\].