<prompt> Hlophisa mofuta oa ntlha boholo, bonyane, kapa che sebakeng sa bohlokoa sa phapano ea equation y3x3 10x2 5.nan  <response>: Instruction in English: Classify the type of point maximum, minimum, or none at the critical point of the differential equation y3x3 10x2 5. . Response in English: 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. . Response in Sesotho: Ha re fumane motso oa tsebetso: y ddx 3x3 10x2 5 9x2 20x Joale, re tla fumana lintlha tsa bohlokoa moo derivative e leng 0 kapa e sa hlalosoang: 9x 2 20x 0 x 9x 20 0 x1 0, x2 -209 E le ho fumana hore na lintlha tsa bohlokoa ke boholo ba sebaka kapa bonyane, re tla fumana motsoako oa bobeli: y d2ydx2 ddx 9x2 20x 18x 20 Joale re tla lekola motsoako oa bobeli sebakeng se seng le se seng sa bohlokoa ho fumana hore na ke boholo, bonyane, kapa ha bo joalo: - Ho x1 0, re na le y0 20 0, kahoo x1 0 ke bonyane ba sebaka. - Ho x2 -209, re na le y-209 18-209 20 -20 0, ka hona x2 -209 ke boholo ba sebaka. Qetellong, mosebetsi y 3x3 10x2 5 o na le bonyane ba sebaka sa x1 0, le boholo ba sebaka sa x2 -209. 