What is the extreme f(x)=-2x^3+21x^2-36x+3 ?

The extreme f(x)=-2x^3+21x^2-36x+3 is Minimum(1,-14),Maximum(6,111)

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extreme f(x)=-2x^3+21x^2-36x+3

extreme points

f (x) = - 2 x^{3} + 21 x^{2} - 36 x + 3

Minimum (1, - 14), Maximum (6, 111)

Solution steps

f^{'} (x) = - 6 x^{2} + 42 x - 36

Find intervals:

Decreasing

: - \infty < x < 1,

Increasing

: 1 < x < 6,

Decreasing

: 6 < x < \infty

Plug

x = 1

into

- 2 x^{3} + 21 x^{2} - 36 x + 3 : - 14

Minimum (1, - 14)

Plug

x = 6

into

- 2 x^{3} + 21 x^{2} - 36 x + 3 : 111

Maximum (6, 111)

Minimum (1, - 14), Maximum (6, 111)

f (x) = 3 x^{2} + 5 y^{2} - 10 x y - 6 y + 1

9600 + 280 x - 10 x^{2}

4 x^{3} + 9 x^{2} - 54 x + 6

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

What is the extreme f(x)=-2x^3+21x^2-36x+3 ?
The extreme f(x)=-2x^3+21x^2-36x+3 is Minimum(1,-14),Maximum(6,111)