What is the extreme f(x)=-4x^3+12x^2-10 ?

The extreme f(x)=-4x^3+12x^2-10 is Minimum(0,-10),Maximum(2,6)

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extreme f(x)=-4x^3+12x^2-10

extreme points

f (x) = - 4 x^{3} + 12 x^{2} - 10

Minimum (0, - 10), Maximum (2, 6)

Solution steps

f^{'} (x) = - 12 x^{2} + 24 x

Find intervals:

Decreasing

: - \infty < x < 0,

Increasing

: 0 < x < 2,

Decreasing

: 2 < x < \infty

Plug

x = 0

into

- 4 x^{3} + 12 x^{2} - 10 : - 10

Minimum (0, - 10)

Plug

x = 2

into

- 4 x^{3} + 12 x^{2} - 10 : 6

Maximum (2, 6)

Minimum (0, - 10), Maximum (2, 6)

f (x) = 2 x + 7 ln (x)

68 - 11

f (x) = x^{3} - 75 x + 3

y = (x - 5)^{2} - 4

- (x + 1) (x - 1)^{2}

What is the extreme f(x)=-4x^3+12x^2-10 ?
The extreme f(x)=-4x^3+12x^2-10 is Minimum(0,-10),Maximum(2,6)