logo88
Answered

At Westonci.ca, we connect you with experts who provide detailed answers to your most pressing questions. Start exploring now! Connect with a community of experts ready to help you find accurate solutions to your questions quickly and efficiently. Get precise and detailed answers to your questions from a knowledgeable community of experts on our Q&A platform.

ex 2.6
8. find the stationary points on the curve y=3x^4 -4x³ -12x² +1 and determine whether they are maximum or minimum turning points

Sagot :

konrad509
[tex]y=3x^4 -4x^3 -12x^2 +1\\ y'=12x^3-12x^2-24x\\\\ 12x^3-12x^2-24x=0\\ 12x(x^2-x-2)=0\\ 12x(x^2+x-2x-2)=0\\ 12x(x(x+1)-2(x+1))=0\\ 12x(x-2)(x+1)=0\\ x=0 \vee x=2 \vee x=-1\\\\ \forall{x\in(-\infty,-1)\cup(0,2)}\ y'<0\Rightarrow y\searrow\\ \forall{x\in(-1,0)\cup(2,\infty)}\ y'>0\Rightarrow y\nearrow\\ \Downarrow\\ y(0)=1=y_{max}\\ y(2)=3\cdot2^4-4\cdot2^3-12\cdot2^2+1=48-32-48=-32=y_{min}[/tex]
[tex]y(-1)=3\cdot(-1)^4-4\cdot(-1)^3-12\cdot(-1)^2+1=3+4-12+1=-4=\\ =y_{min}[/tex]
We appreciate your time on our site. Don't hesitate to return whenever you have more questions or need further clarification. We hope our answers were useful. Return anytime for more information and answers to any other questions you have. We're glad you visited Westonci.ca. Return anytime for updated answers from our knowledgeable team.