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Question Number 169447 by Mastermind last updated on 30/Apr/22

The equation of the curve is given  y=(x^3 /6)−((5x^2 )/2)−6x−1  1) Determine the critical points  2) Distinguish between these points  3) Determine the Maximum and  minimum values  4) Determine the value of x and y  at point of inflexion     Mastermind

$${The}\:{equation}\:{of}\:{the}\:{curve}\:{is}\:{given} \\ $$$${y}=\frac{{x}^{\mathrm{3}} }{\mathrm{6}}−\frac{\mathrm{5}{x}^{\mathrm{2}} }{\mathrm{2}}−\mathrm{6}{x}−\mathrm{1} \\ $$$$\left.\mathrm{1}\right)\:{Determine}\:{the}\:{critical}\:{points} \\ $$$$\left.\mathrm{2}\right)\:{Distinguish}\:{between}\:{these}\:{points} \\ $$$$\left.\mathrm{3}\right)\:{Determine}\:{the}\:{Maximum}\:{and} \\ $$$${minimum}\:{values} \\ $$$$\left.\mathrm{4}\right)\:{Determine}\:{the}\:{value}\:{of}\:{x}\:{and}\:{y} \\ $$$${at}\:{point}\:{of}\:{inflexion}\: \\ $$$$ \\ $$$${Mastermind} \\ $$

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