Question Number 159874 by tounghoungko last updated on 22/Nov/21
$$\:\:\:\:{Given}\:{the}\:{curve}\:{y}={x}^{\mathrm{4}} +\mathrm{3}{x}^{\mathrm{3}} −\mathrm{6}{x}^{\mathrm{2}} −\mathrm{3}{x} \\ $$$$\:{determine}\:{for}\:{which}\:{value}\: \\ $$$$\:{of}\:\alpha\:{the}\:{tangent}\:{to}\:{the}\:{curve} \\ $$$$\:{from}\:{point}\:{P}\left(\alpha,\mathrm{0}\right)\:{is}\:{maximum}. \\ $$
Commented by mr W last updated on 22/Nov/21
$${what}\:{do}\:{you}\:{mean}\:{with}\:``{the}\:{tangent} \\ $$$${to}\:{the}\:{curve}\:{is}\:{maximum}''? \\ $$
Commented by tounghoungko last updated on 22/Nov/21
$${the}\:{tangent}\:{with}\:{slope}\:{maximum} \\ $$
Commented by mr W last updated on 22/Nov/21
$${no}\:{solution}!\: \\ $$$${since}\:{when}\:{x}\rightarrow+\infty,\:{y}'\rightarrow+\infty \\ $$