What is the extreme f(x)= 1/4 x^4-2x^3-18x^2+216x ?

The extreme f(x)= 1/4 x^4-2x^3-18x^2+216x is Minimum(-6,-1188),Saddle(6,540)

Popular >

extreme f(x)= 1/4 x^4-2x^3-18x^2+216x

extreme points

f (x) = \frac{1}{4} x^{4} - 2 x^{3} - 18 x^{2} + 216 x

Minimum (- 6, - 1188), Saddle (6, 540)

Solution steps

f^{'} (x) = x^{3} - 6 x^{2} - 36 x + 216

Find intervals:

Decreasing

: - \infty < x < - 6,

Increasing

: - 6 < x < 6,

Increasing

: 6 < x < \infty

Plug

x = - 6

into

\frac{1}{4} x^{4} - 2 x^{3} - 18 x^{2} + 216 x : - 1188

Minimum (- 6, - 1188)

Plug

x = 6

into

\frac{1}{4} x^{4} - 2 x^{3} - 18 x^{2} + 216 x : 540

Saddle (6, 540)

Minimum (- 6, - 1188), Saddle (6, 540)

f (x, y) = 3 x^{(2)} y - 8 x y^{(3)} + 6 y^{(3)}

f (x) = - 2 x y - 8 x^{2} - 2 y^{2} - 86 x + 8 y + 9

y = 2 x + sin (4 x), - \frac{π}{3} \leq x \leq \frac{π}{3}

x^{2} + 10 x + 24

What is the extreme f(x)= 1/4 x^4-2x^3-18x^2+216x ?
The extreme f(x)= 1/4 x^4-2x^3-18x^2+216x is Minimum(-6,-1188),Saddle(6,540)