<prompt> Classify the type of point maximum, minimum, or none at the critical point of the differential equation y3x3 10x2 5.  <response>: Lets find the derivative of the function:y ddx 3x3 10x2 5 9x2 20xThen, we will find the critical points where the derivative is 0 or undefined:9x2 20x 0x 9x 20 0x1 0, x2 -209In order to determine whether the critical points are a local maximum or minimum, we will find the second derivative:y d2ydx2 ddx 9x2 20x 18x 20Now we will evaluate the second derivative at each critical point to determine if they are a maximum, minimum, or neither:- At x1 0, we have y0 20 0, therefore x1 0 is a local minimum.- At x2 -209, we have y-209 18-209 20 -20 0, therefore x2 -209 is a local maximum.In conclusion, the function y 3x3 10x2 5 has a local minimum at x1 0, and a local maximum at x2 -209. 