class 12

Math

Calculus

Application of Derivatives

Given $P(x)=x_{4}+ax_{3}+cx+d$such that $x=0$is the only real root of \displaystyle{P}'{\left({x}\right)}\text{}=\text{}{0}.\text{}{I}{f}\text{}{P}

- ""<""P(1)$,then∈the∫erval$[1,""1]\displaystyle.{\left({1}\right)}{P}{\left({1}\right)}{i}{s}{t}{h}{e}\min{i}\mu{m}{\quad\text{and}\quad}{P}{\left({1}\right)}{i}{s}{t}{h}{e}\max{i}\mu{m}{o}{f}{P}|{\left|{P}{\left({1}\right)}{i}{s}\neg\min{i}\mu{m}{b}{u}{t}{P}{\left({1}\right)}{i}{s}{t}{h}{e}\max{i}\mu{m}{o}{f}{P}|{\left|{P}{\left({1}\right)}{i}{s}{t}{h}{e}\min{i}\mu{m}{b}{u}{t}{P}{\left({1}\right)}{i}{s}\neg{t}{h}{e}\max{i}\mu{m}{o}{f}{P}|{\left|\ne{i}{t}{h}{e}{r}{P}{\left({1}\right)}{i}{s}{t}{h}{e}\min{i}\mu{m}{n}{\quad\text{or}\quad}{P}{\left({1}\right)}{i}{s}{t}{h}{e}\max{i}\mu{m}{o}{f}{P}\right.}\right.}\right.}