The derivative of a certain continuous and differentiable function is given by:y′=3−x2−22−x+9Analyze the function and create a sketch of the original if the only zeros are at x=0 and x=3.

Question

ithangesf4 · Accepted Answer

Step 1For maxima-minima, derivative of the function must be zero. That is,y′=03x2−12x+9=0x2−4x+3=0(x−3)(x−1)=0x=1, 3Now, the function has maxima minima at x=1 and x=3Now, second order derivative of the function is given by,y″=ddx(3x2−12x+9)=6x−12Now,y″|{x=1}=6x−12|x=1=6−12=−6&amp;lt;0Thus, the function has maxima at x=1y″|{x=3}=6x−12|x=3=18−12=6&amp;gt;0Thus, the function has minima at x=3

The derivative of a certain continuous and differentiable function is

Answered question

Answer & Explanation

New Questions in Calculus 1