Question

If y = x^3 -3x. Find the value of y at its local maxima.​

Answer 1

Answer:

Local maximum value = 2

Explanation:

If y = x^3 -3x. Find the value of y at its local maxima.​

$y = x^3 -3x$

$y'=3x^2-3$

$y''=6x$

$y'=0$

$\implies\;3x^2-3=0$

$\implies\;x^2-1=0$

$\implies\;x^2=1$

$\implies\;x=\pm1$

when x=1

$y''=6>0$

$\implies\:\text{y has local minimum at x=1}$

when x=-1

$y''=-6<0$

$\implies\:\text{y has local maximum at x=-1}$

$\therefore\text{Local maximum}=(-1)^3-3(-1)=-1+3=2$