Discover the answers to your questions at Westonci.ca, where experts share their knowledge and insights with you. Get quick and reliable solutions to your questions from a community of seasoned experts on our user-friendly platform. Discover detailed answers to your questions from a wide network of experts on our comprehensive Q&A platform.
Sagot :
Given: The function below
[tex]f(x)=2x^4+26x^3-42x^2+7[/tex]To Determine: The interval of the inflection points
Solution:
The inflection points is the point where the second derivative of the function is equal to zero
Step 1: Determine the first derivative
[tex]\begin{gathered} f(x)=2x^4+26x^3-42x^2+7 \\ f^{\prime}(x)=8x^3+76x^2-84x \end{gathered}[/tex]Step 2: Determine the second derivative
[tex]\begin{gathered} f^{\prime}(x)=8x^3+78x^2-84x \\ f^{\prime}^{\prime}(x)=24x^2+156x-84 \end{gathered}[/tex]Step 3: Equate the second derivative to zero
[tex]24x^2+156x-84=0[/tex][tex]\begin{gathered} 24x^2-12x+168x-84=0 \\ 12x(2x-1)+84(2x-1)=0 \\ (2x-1)(12x+84)=0 \\ 2x-1=0,or12x+84=0 \\ 2x=1,or12x=-84 \\ x=\frac{1}{2},or\text{ }x=-\frac{84}{12} \\ x=\frac{1}{2},or\text{ }x=-7 \end{gathered}[/tex][tex]undefined[/tex]
We hope this information was helpful. Feel free to return anytime for more answers to your questions and concerns. Thank you for visiting. Our goal is to provide the most accurate answers for all your informational needs. Come back soon. Westonci.ca is committed to providing accurate answers. Come back soon for more trustworthy information.
