Find the values of for which f(x)= cases 4x-x^3+ (a^2-3a+3),&0 x<3 -18,&x 3 cases has…

MATHEMATICS · Subjective · CBSE · Mathematics · Applications of Derivatives · Applications of Derivatives

Problem

Find the values of

a

for which

f(x)=\begin{cases}4x-x^3+\log(a^2-3a+3),&0\leq x<3\\x-18,&x\geq3\end{cases}

has a local maximum at

x=3