What is the extreme f(x)=2x^3-27x^2+84x+6 ?

The extreme f(x)=2x^3-27x^2+84x+6 is Maximum(2,82),Minimum(7,-43)

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extreme f(x)=2x^3-27x^2+84x+6

extreme points

f (x) = 2 x^{3} - 27 x^{2} + 84 x + 6

Maximum (2, 82), Minimum (7, - 43)

Solution steps

f^{'} (x) = 6 x^{2} - 54 x + 84

Find intervals:

Increasing

: - \infty < x < 2,

Decreasing

: 2 < x < 7,

Increasing

: 7 < x < \infty

Plug

x = 2

into

2 x^{3} - 27 x^{2} + 84 x + 6 : 82

Maximum (2, 82)

Plug

x = 7

into

2 x^{3} - 27 x^{2} + 84 x + 6 : - 43

Minimum (7, - 43)

Maximum (2, 82), Minimum (7, - 43)

x^{2} + x y + y^{2} - 7 y + 16

\frac{a}{6 x ^{2} - x ^{3}}

P (x, y) = 15 x^{2} + 14 x y + 3 y^{2} + 41 x + 23 y + 14

8 x^{2} - 4 x^{4}

f (x) = \frac{5 x}{e ^{2 x^{2} + 3}}

What is the extreme f(x)=2x^3-27x^2+84x+6 ?
The extreme f(x)=2x^3-27x^2+84x+6 is Maximum(2,82),Minimum(7,-43)