What is the extreme f(x)=-12x^3+2x^2-3 ?

The extreme f(x)=-12x^3+2x^2-3 is Minimum(0,-3),Maximum(1/9 ,-727/243)

Popular >

extreme f(x)=-12x^3+2x^2-3

extreme points

f (x) = - 12 x^{3} + 2 x^{2} - 3

Minimum (0, - 3), Maximum (\frac{1}{9}, - \frac{727}{243})

Solution steps

f^{'} (x) = - 36 x^{2} + 4 x

Find intervals:

Decreasing

: - \infty < x < 0,

Increasing

: 0 < x < \frac{1}{9},

Decreasing

: \frac{1}{9} < x < \infty

Plug

x = 0

into

- 12 x^{3} + 2 x^{2} - 3 : - 3

Minimum (0, - 3)

Plug

x = \frac{1}{9}

into

- 12 x^{3} + 2 x^{2} - 3 : - \frac{727}{243}

Maximum (\frac{1}{9}, - \frac{727}{243})

Minimum (0, - 3), Maximum (\frac{1}{9}, - \frac{727}{243})

f (x) = x^{3} - 2 x^{2} - 15 x + 10 [- 2]

f (x, y) = x^{2} - y^{2} + x y - 5 x

y = \frac{1}{2} x^{2} + (\frac{14 - 3 x}{4})^{2}

93000 x - 36000

f (x) = x^{4} - 32 x^{2} - 10

What is the extreme f(x)=-12x^3+2x^2-3 ?
The extreme f(x)=-12x^3+2x^2-3 is Minimum(0,-3),Maximum(1/9 ,-727/243)