Text Find the stationary points of y=x3−3x2−9x+5y=x^{3}-3x^{2}-9x+5y=x3−3x2−9x+5 and classify them as relative maxima or minima. Solution y′=3x2−6x−9=3(x−3)(x+1)=0⇒x=−1, x=3y'=3x^{2}-6x-9=3(x-3)(x+1)=0\Rightarrow x=-1,\ x=3y′=3x2−6x−9=3(x−3)(x+1)=0⇒x=−1, x=3. y′′=6x−6y''=6x-6y′′=6x−6: y′′(−1)=−12<0y''(-1)=-12<0y′′(−1)=−12<0 (max), y′′(3)=12>0y''(3)=12>0y′′(3)=12>0 (min). y(−1)=10y(-1)=10y(−1)=10; y(3)=−22y(3)=-22y(3)=−22. max (−1,10);min (3,−22)\boxed{\text{max }(-1,10);\quad \text{min }(3,-22)}max (−1,10);min (3,−22)