Question

find the maximum and minimum values of 4x^3+9x^2-12x+1​

Answer 1

$\huge\color{lime}\ \boxed{\colorbox{black}{Answer : ♞ }}$

$= > 4x ^ { 3 } +9x ^ { 2 } -12x+1$

The derivative of a polynomial is the sum of the derivatives of its terms. The derivative of a constant term is 0. The derivative of

$ax^{n} \: is \: \: nax^{n-1}.$

$= > 3\times 4x^{3-1}+2\times 9x^{2-1}-12x^{1-1}$

$\color{red}Multiply \: 3 \: times \: 4.$

$= > 12x^{3-1}+2\times 9x^{2-1}-12x^{1-1}$

$\color{red}Subtract \: 1 \: from \: 3.$

$= > 12x^{2}+2\times 9x^{2-1}-12x^{1-1}$

$\color{red}Multiply \: 2 \: times \: 9.$

$= > 12x^{2}+18x^{2-1}-12x^{1-1}$

$\color{red}Subtract \: 1 \: from \: 2.$

$= > 12x^{2}+18x^{1}-12x^{1-1}$

$\color{red}Subtract \: 1 \: from \: 1.$

$= > 12x^{2}+18x^{1}-12x^{0}$

$\color{red}For \: any \: term \: t, \: t^{1}=t.$

$= > 12x^{2}+18x-12x^{0}$

$\color{red}For \: any \: term \: t \: except \: 0, t^{0}=1.$