What is the extreme f(x)=-2x^3+3x^2+12x-5 ?

The extreme f(x)=-2x^3+3x^2+12x-5 is Minimum(-1,-12),Maximum(2,15)

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extreme f(x)=-2x^3+3x^2+12x-5

extreme points

f (x) = - 2 x^{3} + 3 x^{2} + 12 x - 5

Minimum (- 1, - 12), Maximum (2, 15)

Solution steps

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

Find intervals:

Decreasing

: - \infty < x < - 1,

Increasing

: - 1 < x < 2,

Decreasing

: 2 < x < \infty

Plug

x = - 1

into

- 2 x^{3} + 3 x^{2} + 12 x - 5 : - 12

Minimum (- 1, - 12)

Plug

x = 2

into

- 2 x^{3} + 3 x^{2} + 12 x - 5 : 15

Maximum (2, 15)

Minimum (- 1, - 12), Maximum (2, 15)

f (x) = - x^{2} + 3 x + 1

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

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

f (x, y) = ln (x) y

f (x, y) = 1 - \frac{x ^{2}}{4} - \frac{y ^{2}}{4}

What is the extreme f(x)=-2x^3+3x^2+12x-5 ?
The extreme f(x)=-2x^3+3x^2+12x-5 is Minimum(-1,-12),Maximum(2,15)