What is the extreme 2x^3-3x^2-12x+18 ?

The extreme 2x^3-3x^2-12x+18 is Maximum(-1,25),Minimum(2,-2)

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extreme 2x^3-3x^2-12x+18

extreme points

2 x^{3} - 3 x^{2} - 12 x + 18

Maximum (- 1, 25), Minimum (2, - 2)

Solution steps

f^{'} (x) = 6 x^{2} - 6 x - 12

Find intervals:

Increasing

: - \infty < x < - 1,

Decreasing

: - 1 < x < 2,

Increasing

: 2 < x < \infty

Plug

x = - 1

into

2 x^{3} - 3 x^{2} - 12 x + 18 : 25

Maximum (- 1, 25)

Plug

x = 2

into

2 x^{3} - 3 x^{2} - 12 x + 18 : - 2

Minimum (2, - 2)

Maximum (- 1, 25), Minimum (2, - 2)

f (x) = e^{- x^{6}}, - 2 \leq x \leq 1

f (x) = x^{6} - 3 x^{4}

f (x, y) = 4 e^{- 5 x - 5 y}

f (x, y) = x^{2} + 3 x y + 4 y^{2} - 6 x + 2 y

f (x) = 250 + 8 x^{3} + x^{4}

What is the extreme 2x^3-3x^2-12x+18 ?
The extreme 2x^3-3x^2-12x+18 is Maximum(-1,25),Minimum(2,-2)