What is the extreme f(x)=2x^3-27x^2+84x+9 ?

The extreme f(x)=2x^3-27x^2+84x+9 is Maximum(2,85),Minimum(7,-40)

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extreme f(x)=2x^3-27x^2+84x+9

extreme points

f (x) = 2 x^{3} - 27 x^{2} + 84 x + 9

Maximum (2, 85), Minimum (7, - 40)

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 + 9 : 85

Maximum (2, 85)

Plug

x = 7

into

2 x^{3} - 27 x^{2} + 84 x + 9 : - 40

Minimum (7, - 40)

Maximum (2, 85), Minimum (7, - 40)

f (x, y) = - 14 + 5 x^{2} + x y + y^{2}

f (x) = \frac{x ^{2}}{( x - 2 ) ^{2}}

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

f (x) = - 6 cos (x - 2 π)

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

What is the extreme f(x)=2x^3-27x^2+84x+9 ?
The extreme f(x)=2x^3-27x^2+84x+9 is Maximum(2,85),Minimum(7,-40)