Explanation

$f(x) = x^3 - 12x + 5$

to find the maximum value, first we differentiate the given function $f(x)$

i.e $\frac {df(x)}{dx} = 3x^2 - 12$

at the minimum point it is $\frac {df(x)}{dx} = 0$

$3x^2 - 12 = 0$

$3x^2 = 12$

$x^2 = 12/3$

$x = ± 2$

to obtain the minimum value,

put x = -2 into $f(x)$

$f(2) = (-2)^3 - 12(-2) + 5$

= $-8 + 24 + 5$

= $29 - 8 = 21$

$f(x) = x^3 - 12x + 5$

to find the maximum value, first we differentiate the given function $f(x)$

i.e $\frac {df(x)}{dx} = 3x^2 - 12$

at the minimum point it is $\frac {df(x)}{dx} = 0$

$3x^2 - 12 = 0$

$3x^2 = 12$

$x^2 = 12/3$

$x = ± 2$

to obtain the minimum value,

put x = -2 into $f(x)$

$f(2) = (-2)^3 - 12(-2) + 5$

= $-8 + 24 + 5$

= $29 - 8 = 21$