Question

Find about maxima & minima $f\left(x\right)=2x^3-15x^2+36x+1$

Answer 1

$f\left(x\right)=2x^3-15x^2+36x+1$

Differentiate wrt to x,

$f^{\prime }\left(x\right)=6x^2-30x+36$

$\therefore f^{\prime }\left(x\right)=0$

$\therefore 6x^2-30x+36=0$

$\therefore x^2-5x+6=0$

$\therefore (x-2)(x+3)=0$

$\therefore x=2,3$

$\therefore f\left(2\right)=2(2{)}^3-15(2{)}^2+36\left(2\right)+1$

$\therefore f\left(2\right)=16-60+72+1$

$\therefore f\left(2\right)=29$

$\therefore f\left(3\right)=2(3{)}^3-15(3{)}^2+36\left(3\right)+1$

$\therefore f\left(3\right)=54-135+108+1$

$\therefore f\left(x\right)=28$

$\therefore$ Maxima is not defined it tends to $\infty$

Minima is $28$.