The local maximum values of the function \(f(x)=3x^{4}+4x^{3}-12x^{2}+2\) are
Answer & explanation
Correct answer: option 2
\(\begin{aligned}f^{\prime}(x)&=0\\ 12x^{3}+12x^{2}-24x&=0\\ x&=-2,0,1\\ f^{\prime \prime}(x)&=36x^{2}+24x-24\\ f^{\prime \prime}(0)&<0, f^{\prime \prime}(1)>0, f^{\prime \prime}(-2)>0\end{aligned}\)