What is the extreme f(x)=-2x^3+24x^2-42x+7 ?

The extreme f(x)=-2x^3+24x^2-42x+7 is Minimum(1,-13),Maximum(7,203)

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extreme f(x)=-2x^3+24x^2-42x+7

extreme points

f (x) = - 2 x^{3} + 24 x^{2} - 42 x + 7

Minimum (1, - 13), Maximum (7, 203)

Solution steps

f^{'} (x) = - 6 x^{2} + 48 x - 42

Find intervals:

Decreasing

: - \infty < x < 1,

Increasing

: 1 < x < 7,

Decreasing

: 7 < x < \infty

Plug

x = 1

into

- 2 x^{3} + 24 x^{2} - 42 x + 7 : - 13

Minimum (1, - 13)

Plug

x = 7

into

- 2 x^{3} + 24 x^{2} - 42 x + 7 : 203

Maximum (7, 203)

Minimum (1, - 13), Maximum (7, 203)

What is the extreme f(x)=-2x^3+24x^2-42x+7 ?
The extreme f(x)=-2x^3+24x^2-42x+7 is Minimum(1,-13),Maximum(7,203)