Question

Find the maximum and minimum values of the following functions

a) 3X^4 - X^3 +2

b) x^4 – 14x^2 +24x +9

Answer 1

a)

$f'=12x^3-3x^2,$

$f'=0,$

$x=\frac 14\to min,$

$f=\frac{511}{256},$

b)

$f'=4x^3-28x+24,$

$f'=0,$

$x_1=-3\to min,$

$f_1=-108,$

$x_2=1\to max,$

$f_2=20,$

$x_3=2\to min,$

$f_3=17.$